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arXiv:1702.02293 [math.GR]AbstractReferencesReviewsResources

Finite $p$-groups with non-cyclic center have non-inner automorphism of order $p$

Rohit Garg, Deepak Gumber

Published 2017-02-08Version 1

Let $G$ be a finite non-abelian $p$-group. A longstanding conjecture asserts that $G$ admits a non-inner automorphism of order $p$. We confirm the conjecture in case $Z(G)$ is not cyclic. As a consequence, we also find necessary and sufficient conditions on $G$ such that the group of all central automorphisms of $G$ is minimal.

Comments: 3 pages
Categories: math.GR
Subjects: 20D15, 20D45
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