moont14263 Posted November 22, 2012 Posted November 22, 2012 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?
Crimson Sunbird Posted February 4, 2013 Posted February 4, 2013 (edited) 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, 2013 by Crimson Sunbird
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