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Archiv der Mathematik

, Volume 111, Issue 2, pp 113–122 | Cite as

Large abelian normal subgroups

  • S. Aivazidis
  • I. M. IsaacsEmail author
Article
  • 137 Downloads

Abstract

In this paper we study the family of finite groups with the property that every maximal abelian normal subgroup is self-centralizing. It is well known that this family contains all finite supersolvable groups, but it also contains many other groups. In fact, every finite group G is a subgroup of some member \(\Gamma \) of this family, and we show that if G is solvable, then \(\Gamma \) can be chosen so that every abelian normal subgroup of G is contained in some self-centralizing abelian normal subgroup of \(\Gamma \).

Keywords

Self-centralizing Supersolvable residual Wreath product Abelian normal subgroup 

Mathematical Subject Classification

20D10 20D99 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.AthensGreece
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA

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