Finite groups which are c-absolute central factor group and the union of Ac-centralizers

Author:

Alamshahi Esmat1,Moghaddam Mohammad Reza R.123,Saeedi Farshid1

Affiliation:

1. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

2. Department of Mathematics, Khayyam University, Mashhad, Iran

3. Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran

Abstract

Let [Formula: see text] be a group and [Formula: see text] be the [Formula: see text]-absolute center of [Formula: see text], that is, the set of all elements of [Formula: see text] fixed by all class preserving automorphisms of [Formula: see text]. In this paper, we classify all finite groups [Formula: see text], whose [Formula: see text]-absolute central factors are isomorphic to the direct product of cyclic groups, [Formula: see text] and [Formula: see text]. Moreover, we consider finite groups which can be written as the union of centralizers of class preserving automorphisms and study the structure of [Formula: see text] for groups, in which the number of distinct centralizers of class preserving automorphisms is equal to 4 or 5.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

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