Let G be a finite group.

A group G is simple if the only normal subgroups of G are the identity and .

What does mean for a group G to be nonabelian simple group?

What does mean for a group G to be not nonabelian simple group?

A nonabelian simple group is a group that is simple (has no normal subgroups other than the trivial subgroup and itself) and nonabelian (not commutative). The smallest nonabelian finite simple group is [latex]A_5[/latex], the alternating group of degree 5, which has order 60.

A finite group that is not a nonabelian simple group is either not simple (has a nontrivial proper normal subgroup) or abelian (commutative) or both. Examples of abelian finite simple groups are cyclic groups of prime orders.

Edited February 4, 201312 yr by Crimson Sunbird