It is a very common exercise in elementary group theory to prove that if ${\rm Aut}(G)$ is cyclic then $G$ is abelian. The usual proof seems to not require it to be cyclic but just locally cyclic. Is this correct? Are there any interesting further generalizations?
2026-04-01 20:04:29.1775073869
If ${\rm Aut}(G)$ is locally cyclic then $G$ is abelian
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