On the maximum number of the pairwise noncommuting elements in a finite group

Author:

Jafarian Amiri Seyyed Majid1,Madadi Halimeh1

Affiliation:

1. Department of Mathematics, Faculty of Sciences, University of Zanjan, P. O. Box 45371-38791, Zanjan, Iran

Abstract

For a finite group [Formula: see text], let [Formula: see text] be the maximum size of a set of pairwise noncommuting elements in [Formula: see text]. In this paper, we give an upper bound of [Formula: see text] for an arbitrary nilpotent group [Formula: see text]. As an application of this result, we give a partial answer to Question 2.8 of [A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq. 7(2) (2000) 139–146]. Also we compute [Formula: see text] when [Formula: see text] is a Frobenius group. Finally we describe structural properties of all groups [Formula: see text] with [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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