Editing Permutation group (section)

==History==
{{main|History of group theory}}

The study of [[Group (mathematics)|groups]] originally grew out of an understanding of permutation groups.<ref>{{harvnb|Dixon|Mortimer|1996|loc=p. 28}}</ref> [[Permutation]]s had themselves been intensively studied by [[Lagrange]] in 1770 in his work on the algebraic solutions of polynomial equations. This subject flourished and by the mid 19th century a well-developed theory of permutation groups existed, codified by [[Camille Jordan]] in his book ''Traité des Substitutions et des Équations Algébriques'' of 1870. Jordan's book was, in turn, based on the papers that were left by [[Évariste Galois]] in 1832.

When [[Arthur Cayley|Cayley]] introduced the concept of an [[abstract group]], it was not immediately clear whether or not this was a larger collection of objects than the known permutation groups (which had a definition different from the modern one). Cayley went on to prove that the two concepts were equivalent in Cayley's theorem.<ref>{{harvnb|Cameron|1994|loc=p. 226}}</ref>

Another classical text containing several chapters on permutation groups is [[William Burnside|Burnside]]'s ''Theory of Groups of Finite Order'' of 1911.<ref>{{citation|first=William|last=Burnside|title=Theory of Groups of Finite Order|year=1955|orig-year=1911|edition=2nd|publisher=Dover}}</ref> The first half of the twentieth century was a fallow period in the study of group theory in general, but interest in permutation groups was revived in the 1950s by [[H. Wielandt]] whose German lecture notes were reprinted as ''Finite Permutation Groups'' in 1964.<ref>{{citation|first=H.|last=Wielandt|title=Finite Permutation Groups|year=1964|publisher=Academic Press}}</ref>