Research Article

On central automorphisms of finite p-groups of class 2

Published in: Quaestiones Mathematicae
Volume 46 , issue 9 , 2023 , pages: 1981–1990

DOI: 10.2989/16073606.2022.2112630

Author(s): M. Shabani-Attar Payame Noor University, Iran

Keywords: Primary: 20D45 , Secondary: 20D15 , Central automorphisms , finite p-groups

Abstract

Let G be a finite p-group and let Aut _c (G) be the group of all central automorphisms of G. Let be the set of all central automorphisms of G fixing Z(G) elementwise. For a finite p-group of class 2, we have . In [6] we proved if and only if Z(G) is cyclic. In this paper we first prove that there is no finite p-group of class 2 for which , and then we characterize the finite p-groups G satisfying . As a consequence, we prove the main results of Curran and McCaughan [2].

« Generating solutions of a linear equation and structure of elements of the Zelisko group II

Cross-section measures, radii, and Radon curves »