Existence of noninner automorphisms of order \(p\) in some finite \(p\)-groups

Authors

  • M. Shabani-Attar University of Payame Noor

Keywords:

Non-inner automorphisms of order $p$, $p$-groups

Abstract

Let \(G\) be a nonabelian finite \(p\)-group of order \(p^m\). A longstanding conjecture asserts that \(G\) admits a noninner automorphism of order $p$. In this paper we prove the validity of the conjecture if, $\exp(G)=p^{m-2}$. Also we show that if $G$ is a finite $p$-group of maximal class, then $G$ has at least $p (p-1)$ non-inner automorphisms of order $p$ which fixes $\Phi(G)$ elementwise. 10.1017/S0004972712000718

Published

2013-02-24

Issue

Vol. 87 No. 2 (2013)

Section

Articles
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