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== References == {{refbegin|30em}} === General references === * {{Citation | last1=Artin | first1=Michael | author-link1=Michael Artin | title=Algebra | publisher=[[Prentice Hall]] | isbn=978-0-13-468960-9 | year=2018 }}, Chapter 2 contains an undergraduate-level exposition of the notions covered in this article. * {{Citation |last=Cook |first=Mariana R. |year=2009 |title=Mathematicians: An Outer View of the Inner World |publisher=Princeton University Press |location=Princeton, N.J. | isbn=978-0-691-13951-7 |url=https://books.google.com/books?id=06h8NT77OgMC&q=Richard+Ewen+Borcherds&pg=PA24 }} * {{Citation | author-link=George G. Hall | last=Hall | first=G. G. | title=Applied Group Theory | publisher=American Elsevier Publishing Co., Inc., New York | mr=0219593 | year=1967}}, an elementary introduction. * {{Citation | last1=Herstein | first1=Israel Nathan |author-link1 = Israel Nathan Herstein | title=Abstract Algebra | publisher=Prentice Hall Inc. | location=Upper Saddle River, NJ | edition=3rd | isbn=978-0-13-374562-7 | mr=1375019 | year=1996}}. * {{Citation | last1=Herstein | first1=Israel Nathan |author-link1 = Israel Nathan Herstein | title=Topics in Algebra | publisher=Xerox College Publishing | location=Lexington, Mass. | edition=2nd | mr=0356988 | year=1975}}. * {{Lang Algebra}}<!-- Don't add a fullstop here: it breaks the layout! --> * {{Citation | last1=Lang | first1=Serge |author-link1 = Serge Lang | title=Undergraduate Algebra | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=3rd | isbn=978-0-387-22025-3 | year=2005}}. * {{Citation | last1=Ledermann | first1=Walter |author-link1 = Walter Ledermann | title=Introduction to the Theory of Finite Groups | publisher=Oliver and Boyd, Edinburgh and London | mr=0054593 | year=1953}}. * {{Citation | last1=Ledermann | first1=Walter |author-link1 = Walter Ledermann | title=Introduction to Group Theory | publisher=Barnes and Noble | location=New York | oclc=795613 | year=1973}}. * {{Citation | last1=Robinson | first1=Derek John Scott |author-link1 = Derek J. S. Robinson | title=A Course in the Theory of Groups | publisher=Springer-Verlag | location=Berlin, New York | isbn=978-0-387-94461-6 | year=1996}}. === Special references === * {{Citation | last1=Artin | first1=Emil | author1-link=Emil Artin | title=Galois Theory | publisher=[[Dover Publications]] | location=New York | isbn=978-0-486-62342-9 | year=1998}}. * {{Citation | last1=Aschbacher | first1=Michael | author1-link = Michael Aschbacher | title=The status of the classification of the finite simple groups | url=https://www.ams.org/notices/200407/fea-aschbacher.pdf | year=2004 | journal=[[Notices of the American Mathematical Society]] | volume=51 | issue=7 | pages=736–740}}. * {{Citation|title=Category Theory| last=Awodey|first=Steve|isbn=978-0-19-958736-0|year=2010|publisher=Oxford University Press}} * {{Citation|title=Biphenyl and bimesityl tetrasulfonic acid – new linker molecules for coordination polymers|first1=Florian|last1=Behler|first2=Mathias S.|last2= Wickleder|first3=Jens|last3=Christoffers|doi=10.3998/ark.5550190.p008.911|journal=Arkivoc|year=2014|volume=2015|issue=2|pages=64–75|doi-access=free|hdl=2027/spo.5550190.p008.911|hdl-access=free}} * {{Citation |title=The Jahn–Teller Effect |first=Isaac |last=Bersuker |isbn=0-521-82212-2 |publisher=Cambridge University Press |year=2006 |url=https://archive.org/details/jahntellereffect0000bers/page/2 }}. * {{Citation | last1=Besche | first1=Hans Ulrich | last2=Eick | first2=Bettina | last3=O'Brien | first3=E. A. | title=The groups of order at most 2000 | url=https://www.ams.org/era/2001-07-01/S1079-6762-01-00087-7/home.html | mr=1826989 | year=2001 | journal=Electronic Research Announcements of the American Mathematical Society | volume=7 | pages=1–4 | doi=10.1090/S1079-6762-01-00087-7| doi-access=free }}. * {{Citation | last1=Bishop | first1=David H. L. | title=Group Theory and Chemistry | publisher=Dover Publications | location=New York | isbn=978-0-486-67355-4 | year=1993}}. * {{Citation | last1=Borel | first1=Armand | author1-link=Armand Borel | title=Linear Algebraic Groups | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | series=Graduate Texts in Mathematics | isbn=978-0-387-97370-8 | mr=1102012 | year=1991 | volume=126}}. * {{Citation | last1=Carter | first1=Roger W. | author1-link=Roger Carter (mathematician) | title=Simple Groups of Lie Type | publisher=[[John Wiley & Sons]] | location=New York | isbn=978-0-471-50683-6 | year=1989}}. * {{Citation | title=The Jahn–Teller Effect in C60 and Other Icosahedral Complexes|first1=C. C.|last1= Chancey|first2=M. C. M.|last2=O'Brien|year=2021|isbn=978-0-691-22534-0|publisher=Princeton University Press}} * {{Citation | last1=Conway | first1=John Horton | author1-link=John Horton Conway | last2=Delgado Friedrichs | first2=Olaf | last3=Huson | first3=Daniel H. | last4=Thurston | first4=William P. | author4-link=William Thurston | title=On three-dimensional space groups | arxiv=math.MG/9911185 | mr=1865535 | year=2001 | journal=Beiträge zur Algebra und Geometrie | volume=42 | issue=2 | pages=475–507}}. * {{Citation | last1=Coornaert | first1=M. | last2=Delzant | first2=T. | last3=Papadopoulos | first3=A. | title=Géométrie et théorie des groupes [Geometry and Group Theory]| publisher=Springer-Verlag | location=Berlin, New York | series=Lecture Notes in Mathematics | isbn=978-3-540-52977-4 | mr=1075994 | year=1990 | volume=1441|language=fr}}. * {{Citation | last1=Denecke | first1=Klaus | last2=Wismath | first2=Shelly L. | title=Universal Algebra and Applications in Theoretical Computer Science | publisher=[[CRC Press]] | location=London | isbn=978-1-58488-254-1 | year=2002}}. * {{Citation |title=Structure and Dynamics: An Atomic View of Materials |first=Martin T|last= Dove |page=265 |isbn=0-19-850678-3 |publisher=Oxford University Press |year=2003 }}. * {{Citation| last=Dudek |first=Wiesław A. |title=On some old and new problems in {{mvar|n}}<!-- not math so it appears correctly colored in the linked title -->-ary groups |journal=Quasigroups and Related Systems |year=2001 |volume=8 |pages= 15–36|mr=1876783|url=https://ibn.idsi.md/sites/default/files/imag_file/15-36_On%20some%20old%20and%20new%20problems%20in%20n-ary%20groups.pdf}}. * {{Citation|title=Stereochemistry of Organic Compounds|last1=Eliel|first1=Ernest|last2=Wilen|first2=Samuel|last3=Mander|first3=Lewis|year=1994 |isbn=978-0-471-01670-0 |publisher=Wiley}} * {{Citation | last = Ellis | first = Graham | contribution = 6.4 Triangle groups | doi = 10.1093/oso/9780198832973.001.0001 | isbn = 978-0-19-883298-0 | mr = 3971587 | pages = 441–444 | publisher = Oxford University Press | title = An Invitation to Computational Homotopy | year = 2019}}. * {{Citation | author-link=Robert Frucht | last1=Frucht | first1=R. | title=Herstellung von Graphen mit vorgegebener abstrakter Gruppe [Construction of graphs with prescribed group] | url=http://www.numdam.org/numdam-bin/fitem?id=CM_1939__6__239_0 | year=1939 | journal=Compositio Mathematica | volume=6 | pages=239–50 | language=de | url-status=dead | archive-url=https://web.archive.org/web/20081201083831/http://www.numdam.org/numdam-bin/fitem?id=CM_1939__6__239_0 | archive-date=2008-12-01 }}. * {{Citation| last1 = Fulton| first1 = William| author1-link = William Fulton (mathematician)| last2 = Harris| first2 = Joe| author2-link = Joe Harris (mathematician)| year = 1991| title = Representation Theory: A First Course| publisher = Springer-Verlag| location = New York| series = [[Graduate Texts in Mathematics]], Readings in Mathematics| volume = 129| isbn = 978-0-387-97495-8| mr = 1153249}} * {{Citation| last = Goldstein | first = Herbert | author-link = Herbert Goldstein | year = 1980 | title = [[Classical Mechanics (Goldstein)|Classical Mechanics]] | edition = 2nd | publisher = Addison-Wesley Publishing | location = Reading, MA | isbn = 0-201-02918-9 | pages = 588–596}}. * {{Citation | last1=Gollmann | first1=Dieter | title=Computer Security | year=2011 | edition=2nd | publisher=John Wiley & Sons, Ltd. | location=West Sussex, England | isbn=978-0-470-74115-3 }} * {{Citation | last1=Hatcher | first1=Allen | author-link=Allen Hatcher | title=Algebraic Topology | url=http://pi.math.cornell.edu/~hatcher/AT/ATpage.html | publisher=[[Cambridge University Press]] | isbn=978-0-521-79540-1 | year=2002}}. * {{Citation | last1=Husain | first1=Taqdir | title=Introduction to Topological Groups | publisher=W.B. Saunders Company | location=Philadelphia | isbn=978-0-89874-193-3 | year=1966}} * {{Citation | last1 = Jahn | first1=H.| author1-link=Hermann Arthur Jahn|last2=Teller|first2=E.|author2-link=Edward Teller| title = Stability of polyatomic molecules in degenerate electronic states. I. Orbital degeneracy | year = 1937 | journal = [[Proceedings of the Royal Society A]] | volume = 161 | issue = 905 | pages = 220–235 | doi = 10.1098/rspa.1937.0142 | bibcode=1937RSPSA.161..220J| doi-access = free }}. * {{Citation | last1=Kuipers | first1=Jack B. | title=Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality | publisher=[[Princeton University Press]] | isbn=978-0-691-05872-6 | mr=1670862 | year=1999| bibcode=1999qrsp.book.....K }}. * {{Citation | last1=Kuga | first1=Michio | author-link=Michio Kuga | title=Galois' Dream: Group Theory and Differential Equations | publisher=Birkhäuser Boston | location=Boston, MA | isbn=978-0-8176-3688-3 | mr=1199112 | year=1993 | url-access=registration | url=https://archive.org/details/galoisdreamgroup0000kuga }}. * {{Citation | last1=Kurzweil | first1=Hans | last2=Stellmacher | first2=Bernd | title=The Theory of Finite Groups | publisher=Springer-Verlag | location=Berlin, New York | series=Universitext | isbn=978-0-387-40510-0 | mr=2014408 | year=2004}}. * {{Citation | last1=Lay | first1=David | title=Linear Algebra and Its Applications | publisher=[[Addison-Wesley]] | isbn=978-0-201-70970-4 | year=2003}}. * {{Citation | last1=Mac Lane | first1=Saunders | author1-link=Saunders Mac Lane | title=[[Categories for the Working Mathematician]] | publisher=Springer-Verlag | location=Berlin, New York | edition=2nd | isbn=978-0-387-98403-2 | year=1998}}. * {{Citation |author-link=Wilhelm Magnus |first1=Wilhelm |last1=Magnus |first2=Abraham |last2=Karrass |first3=Donald |last3=Solitar |title=Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations |url=https://books.google.com/books?id=1LW4s1RDRHQC&pg=PR2 |year=2004 |orig-year=1966 |publisher=Courier |isbn=978-0-486-43830-6 }} * {{Citation|url=https://mathscinet.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=20&co6=AND&pg7=ALLF&s7=&co7=AND&dr=pubyear&yrop=eq&arg3=2020&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&review_format=html&Submit=Suche|title=List of papers reviewed on MathSciNet on "Group theory and its generalizations" (MSC code 20), published in 2020|url-access=registration|access-date=14 May 2021|last=MathSciNet|year=2021}} * {{Citation | last1=Michler | first1=Gerhard | title=Theory of Finite Simple Groups | publisher=Cambridge University Press | isbn=978-0-521-86625-5 | year=2006}}. * {{Citation | last1=Milne | first1=James S. | title=Étale Cohomology | publisher=Princeton University Press | isbn=978-0-691-08238-7 | year=1980 | url=https://archive.org/details/etalecohomology00miln }} * {{Citation | last1=Mumford | first1=David | author1-link=David Mumford | last2=Fogarty | first2=J. | last3=Kirwan | first3=F. | title=Geometric Invariant Theory | publisher=Springer-Verlag | location=Berlin, New York | edition=3rd | isbn=978-3-540-56963-3 | mr=1304906 | year=1994 | volume=34}}. * {{Citation | last1=Naber | first1=Gregory L. | title=The Geometry of Minkowski Spacetime | publisher=Dover Publications | location=New York | isbn=978-0-486-43235-9 | mr=2044239 | year=2003}}. * {{Citation | last = Neukirch| first = Jürgen| author-link = Jürgen Neukirch| title = Algebraic Number Theory| publisher = Springer-Verlag| location = Berlin| series = {{lang|de|Grundlehren der mathematischen Wissenschaften}}| isbn = 978-3-540-65399-8| mr = 1697859| zbl = 0956.11021 | year = 1999| volume = 322}} * {{Citation | last1=Romanowska | first1=A. B.|author1-link=Anna Romanowska | last2=Smith | first2=J. D. H. | title=Modes | publisher=[[World Scientific]] | isbn=978-981-02-4942-7 | year=2002}}. * {{Citation | last1=Ronan | first1=Mark | author1-link= Mark Ronan|title=Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics | publisher=[[Oxford University Press]] | isbn=978-0-19-280723-6 | year=2007}}. * {{Citation | last1=Rosen | first1=Kenneth H. | title=Elementary Number Theory and its Applications | publisher=Addison-Wesley | edition=4th | isbn=978-0-201-87073-2 | mr=1739433 | year=2000}}. * {{Citation| last = Rudin | first = Walter | author-link = Walter Rudin | title = Fourier Analysis on Groups|publisher=Wiley-Blackwell|series=Wiley Classics|year=1990|isbn=0-471-52364-X}}. * {{Citation | last1=Seress | first1=Ákos | title=An Introduction to Computational Group Theory | url=https://www.ams.org/notices/199706/seress.pdf | mr=1452069 | year=1997 | journal=Notices of the American Mathematical Society | volume=44 | issue=6 | pages=671–679}}. * {{Citation | last1=Serre | first1=Jean-Pierre | author1-link=Jean-Pierre Serre | title=Linear Representations of Finite Groups | publisher=Springer-Verlag | location=Berlin, New York | isbn=978-0-387-90190-9 | mr=0450380 | year=1977 | url-access=registration | url=https://archive.org/details/linearrepresenta1977serr }}. * {{Citation | last=Schwartzman | first=Steven | year=1994 | title=The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English | publisher=Mathematical Association of America | isbn=978-0-88385-511-9 }}. * {{Citation | last1=Shatz | first1=Stephen S. | title=Profinite Groups, Arithmetic, and Geometry | publisher=Princeton University Press | isbn=978-0-691-08017-8 | mr=0347778 | year=1972}} * {{Citation|title=An Introduction to Theoretical Chemistry |last1=Simons|first1=Jack|isbn=978-0-521-53047-7|year=2003|publisher=Cambridge University Press}} * {{Citation|last1=Solomon|first1=Ronald|title=The classification of finite simple groups: A progress report|journal=Notices of the AMS|year=2018|volume=65|issue=6|page=1|doi=10.1090/noti1689|doi-access=free}} * {{Citation|last=Stewart |first=Ian |author-link=Ian Stewart (mathematician) |title=Galois Theory |edition=4th |publisher=CRC Press |year=2015 |isbn=978-1-4822-4582-0}} * {{Citation|last = Suzuki|first= Michio|author-link = Michio Suzuki (mathematician)|title = On the lattice of subgroups of finite groups|journal = [[Transactions of the American Mathematical Society]]| volume = 70| issue = 2| year = 1951| pages = 345–371| doi = 10.2307/1990375|jstor = 1990375|doi-access = free}}. * {{Citation | last1=Warner | first1=Frank | title=Foundations of Differentiable Manifolds and Lie Groups | publisher=Springer-Verlag | location=Berlin, New York | isbn=978-0-387-90894-6 | year=1983}}. * {{Weibel IHA|mode=cs2}} * {{Citation | last1=Weinberg | first1=Steven | author1-link=Steven Weinberg | title=Gravitation and Cosmology | publisher=John Wiley & Sons | location=New York | year=1972 | isbn=0-471-92567-5 | url=https://archive.org/details/gravitationcosmo00stev_0 }}. * {{Citation | last1=Welsh | first1=Dominic | author1-link=Dominic Welsh | title=Codes and Cryptography | publisher=Clarendon Press | location=Oxford | isbn=978-0-19-853287-3 | year=1989}}. * {{Citation | last1=Weyl | first1=Hermann | author1-link=Hermann Weyl | title=Symmetry | publisher=Princeton University Press | isbn=978-0-691-02374-8 | year=1952}}. * {{Citation |title=Quantum Field Theory in a Nutshell|title-link=Quantum Field Theory in a Nutshell |first=A.|last=Zee |author-link=Anthony Zee |date=2010|edition=second |publisher=Princeton University Press|isbn=978-0-691-14034-6|location=Princeton, N.J.|oclc=768477138}} === Historical references === {{See also|List of publications in mathematics#Group theory|l1=Historically important publications in group theory}} * {{Citation | last1=Borel | first1=Armand | author1-link=Armand Borel | title=Essays in the History of Lie Groups and Algebraic Groups | publisher=[[American Mathematical Society]] | location=Providence, R.I. | isbn=978-0-8218-0288-5 | year=2001}} * {{Citation | last1=Cayley | first1=Arthur | author1-link=Arthur Cayley | title=The Collected Mathematical Papers of Arthur Cayley | url=http://www.hti.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;cc=umhistmath;rgn=full%20text;idno=ABS3153.0001.001;didno=ABS3153.0001.001;view=image;seq=00000140 | publisher=[[Cambridge University Press]] | year=1889 | volume=II (1851–1860)}}. * {{MacTutor | id=Development_group_theory | class=HistTopics | title = The development of group theory}} * {{Citation | last1=Curtis | first1=Charles W. | author-link = Charles W. Curtis | title=Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer | publisher=American Mathematical Society | location=Providence, R.I. | series=History of Mathematics | isbn=978-0-8218-2677-5 | year=2003}}. * {{Citation | last1=von Dyck | year=1882 | first1=Walther | author1-link=Walther von Dyck | title=Gruppentheoretische Studien (Group-theoretical studies) | doi=10.1007/BF01443322 | journal=[[Mathematische Annalen]] | volume=20 | issue=1 | pages=1–44 | s2cid=179178038 | url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0020&DMDID=DMDLOG_0007&L=1 | language=de | url-status=dead | archive-url=https://web.archive.org/web/20140222213905/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0020&DMDID=DMDLOG_0007&L=1 | archive-date=2014-02-22 }}. * {{Citation | last1=Galois | first1=Évariste | author1-link=Évariste Galois | editor1-last=Tannery | editor1-first=Jules | title=Manuscrits de Évariste Galois [Évariste Galois' Manuscripts] | url=http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAN9280 | publisher=Gauthier-Villars | location=Paris | year=1908|language=fr}} (Galois work was first published by [[Joseph Liouville]] in 1843). * {{Citation | last1=Jordan | first1=Camille | author-link=Camille Jordan | title=Traité des substitutions et des équations algébriques [Study of Substitutions and Algebraic Equations] | url=https://archive.org/details/traitdessubstit00jordgoog | publisher=Gauthier-Villars | location=Paris | year=1870 |language=fr}}. * {{Citation | doi=10.2307/2690312 | last1=Kleiner | first1=Israel | author-link=Israel Kleiner (mathematician) | title=The evolution of group theory: A brief survey | mr=863090 | year=1986 | journal=[[Mathematics Magazine]] | volume=59 | issue=4 | pages=195–215 | jstor=2690312 }}. * {{Citation | last1=Lie | first1=Sophus | author1-link=Sophus Lie | title=Gesammelte Abhandlungen. Band 1 [Collected papers. Volume 1] | publisher=Johnson Reprint Corp. | location=New York | mr=0392459 | year=1973|language=de}}. * {{Citation | last1=Mackey | first1=George Whitelaw | author1-link=George Mackey | title=The Theory of Unitary Group Representations | publisher=[[University of Chicago Press]] | mr=0396826 | year=1976}} * {{Citation | last1=Smith | first1=David Eugene | author1-link=David Eugene Smith | title=History of Modern Mathematics | url=https://www.gutenberg.org/ebooks/8746 | series=Mathematical Monographs, No. 1 | year=1906}}. * {{Citation | last=Weyl | first=Hermann | author-link=Hermann Weyl |title=The Theory of Groups and Quantum Mechanics |publisher=Dover |orig-year=1931 | year = 1950 | bibcode=1950tgqm.book.....W | translator-first=H. P. |translator-last=Robertson | isbn = 978-0-486-60269-1}}. * {{Citation | last1=Wussing | first1=Hans | author-link=Hans Wussing | title=The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory | publisher=[[Dover Publications]] | location=New York | isbn=978-0-486-45868-7 | year=2007}}. {{refend|30em}}
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