Third Term of the Lower Autocentral Series of Abelian Groups

Authors

  • Mohammad Naghshineh
  • Mohammad Reza R. Moghaddam
  • Foroud Parvaneh

Keywords:

Autocommutator subgroup, autocen- tral series, abelian group

Abstract

Let G be a group and Aut(G) be the group of auto- morphisms of G. Then [g, α, β] = (g−1gα)−1(g−1gα)β is the au- tocommutator of the element g ∈ G and α, β ∈ Aut(G) of weight 3. Also, we define K2(G) [g,α,β] : g ∈ G,α,β ∈ Aut(G) > to be the third term of the lower autocentral series of subgroups of G. In this paper, it is shown that every finite abelian group is isomorphic to the third term of the autocentral series of some finite abelian group.

Author Biographies

Mohammad Naghshineh

Department of Mathematics Islamic Azad University, Jahrom-Branch Jahrom, Iran.

Mohammad Reza R. Moghaddam

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

Foroud Parvaneh

Department of Mathematics Islamic Azad University, Kermanshah-Branch Kermanshah, Iran.

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Published

2009-04-01

Issue

Vol 4 (2009-2010)

Section

Vol. 4, No. 1 (2009)

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