R. Garg, “On Commuting Automorphisms of Finite <nobr>$p$</nobr>-Groups with a Metacyclic Quotient”, Mat. Zametki, 2019, Volume 106, Issue 2,Pages <nobr>296

This article is cited in 2 papers

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Brief Communications

On Commuting Automorphisms of Finite $p$-Groups with a Metacyclic Quotient

R. Garg

Govt. Ripudaman College, Nabha, 147 201 India

Abstract: Let $G$ be a finite non-Abelian $p$-group, where $p$ is an odd prime, such that $G/Z(G)$ is metacyclic. We prove that all commuting automorphisms of $G$ form a subgroup of $\text{Aut}(G)$ if and only if $G$ is of nilpotence class 2.

Keywords: commuting automorphism, metacyclic $p$-group.

Received: 17.10.2018
Revised: 17.10.2018

Language: English