Editing List of group theory topics (section)

==Basic types of groups==
{{colbegin|colwidth=22em}}
* [[Examples of groups]]
* [[Abelian group]]
* [[Cyclic group]]
** [[Rank of an abelian group]]
* [[Dicyclic group]]
* [[Dihedral group]]
* [[Divisible group]]
* [[Finitely generated abelian group]]
* [[Group representation]]
* [[Klein four-group]]
* [[List of small groups]]
* [[Locally cyclic group]]
* [[Nilpotent group]]
* [[Non-abelian group]]
* [[Solvable group]]
* [[P-group]]
* [[Pro-finite group]]
{{colend}}

===Simple groups and their classification===
*[[Classification of finite simple groups]]
{{colbegin|colwidth=22em}}
* [[Alternating group]]
* [[Borel subgroup]]
* [[Chevalley group]]
* [[Conway group]]
* [[Feit–Thompson theorem]]
* [[Fischer group]]
* [[General linear group]]
* [[Group of Lie type]]
* [[Group scheme]]
* [[HN group]]
* [[Janko group]]
* [[Lie group]]
** [[Simple Lie group]]
* [[Linear algebraic group]]
* [[List of finite simple groups]]
* [[Mathieu group]]
* [[Monster group]]
** [[Baby Monster group]]
** [[Bimonster]]
* [[Projective group]]
* [[Reductive group]]
* [[Simple group]]
** [[Quasisimple group]]
* [[Special linear group]]
* [[Symmetric group]]
* [[Thompson group (finite)]]
* [[Tits group]]
* [[Weyl group]]
{{colend}}

===Permutation and symmetry groups===
{{colbegin|colwidth=22em}}
* [[Arithmetic group]]
* [[Braid group]]
* [[Burnside's lemma]]
* [[Cayley's Theorem|Cayley's theorem]]
* [[Coxeter group]]
* [[Crystallographic group]]
* [[Crystallographic point group]], [[Schoenflies notation]]
* [[Discrete group]]
* [[Euclidean group]]
* [[Even and odd permutations]]
* [[Frieze group]]
* [[Frobenius group]]
* [[Fuchsian group]]
* [[Geometric group theory]]
* [[Group action (mathematics)|Group action]]
* [[Homogeneous space]]
* [[Hyperbolic group]]
* [[Isometry group]]
* [[Orbit (group theory)]]
* [[Permutation]]
* [[Permutation group]]
* [[Rubik's Cube group]]
* [[Space group]]
* [[Stabilizer subgroup]]
* [[Steiner system]]
* [[Strong generating set]]
* [[Symmetry]]
* [[Symmetric group]]
* [[Symmetry group]]
* [[Wallpaper group]]
{{colend}}