On automorphisms of finite $p$-groups
Hemant Kalra, Deepak Gumber

TL;DR
This paper provides a concise, elementary proof of a known result that for certain finite p-groups, the order of the group divides the order of its automorphism group, specifically when the pair (G, Z(G)) is a Camina pair.
Contribution
It offers a simplified and elementary proof of a previously established theorem relating the size of finite p-groups and their automorphism groups in the Camina pair context.
Findings
The order of G divides the order of Aut(G) for Camina pairs.
The proof is shorter and more elementary than previous proofs.
The result applies to finite p-groups with specific structural properties.
Abstract
It is proved in [J. Group Theory, {\bf 10} (2007), 859-866] that if is a finite -group such that is a Camina pair, then divides . We give a very short and elementary proof of this result.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Geometric and Algebraic Topology
