Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(1): 79-83

Printed January 1, 2011

https://doi.org/10.4134/BKMS.2011.48.1.79

Copyright © The Korean Mathematical Society.

The lower autocentral series of abelian groups

Mohammad Reza R. Moghaddam, Foroud Parvaneh, and Mohammad Naghshineh

Centre of Excellence in Analysis on Algebraic Structures, Islamic Azad University, Islamic Azad University

Abstract

In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $n^{th}$-term of the lower autocentral series of some finite abelian group.

Keywords: autocommutator subgroup, autocentral series, abelian group

MSC numbers: 20D45, 20D25, 20E34