 ==structures and operations==  * central extension * direct product of groups * direct sum of groups * extension problem * free abelian group * free group * free product * generating set of a group * group cohomology * group extension * presentation of a group * product of group subsets * schur multiplier * semidirect product * sylow theorems ** hall subgroup * wreath product  ==basic properties of groups==  *butterfly lemma * center of a group * centralizer and normalizer * characteristic subgroup * commutator * composition series * conjugacy class * conjugate closure * conjugation of isometries in euclidean space * core (group) * coset * derived group * euler's theorem * fitting subgroup **generalized fitting subgroup * hamiltonian group * identity element * lagrange's theorem * multiplicative inverse * normal subgroup * perfect group * p-core * schreier refinement theorem * subgroup * transversal (combinatorics) * torsion subgroup * zassenhaus lemma  ===group homomorphisms===  * automorphism * automorphism group * factor group * fundamental theorem on homomorphisms * group homomorphism * group isomorphism * homomorphism * isomorphism theorem * inner automorphism * order automorphism * outer automorphism group * quotient group  ==basic types of groups==  * 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 * solvable group * p-group * pro-finite group  ===simple groups and their classification=== *classification of finite simple groups  * algebraic group * alternating group * borel subgroup * chevalley group * conway group * feitâthompson theorem * fischer group * general linear group * group of lie type * group scheme * janko group * lie group ** simple lie group * list of finite simple groups * mathieu group * monster group ** baby monster group ** bimonster * parabolic subgroup * projective group * simple group ** quasisimple group * special linear group * symmetric group * thompson group (finite) * tits group * weyl group  ===permutation and symmetry groups===  * arithmetic group * braid group * burnside's lemma * [
Group_theory Mathematics-related_lists Outlines Properties_of_groups