Classification of alternating groups that are N-groups
This article classifies the members in a particular group family alternating group that satisfy the group property N-group.
Similarly, the finitary alternating group on an infinite set is never a N-group.
Proof of failure for larger
For , denote by the alternating group on the set . Let . The normalizer contains the centralizer of , which in turn contains the alternating group on the set , which is isomorphic to , which is simple non-abelian since (see alternating groups are simple). Thus, is not solvable, so is not a N-group.