Large abelian normal subgroups
- 137 Downloads
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 \(\Gamma \).
KeywordsSelf-centralizing Supersolvable residual Wreath product Abelian normal subgroup
Mathematical Subject Classification20D10 20D99
Unable to display preview. Download preview PDF.
- 3.I. M. Isaacs, Character Theory of Finite Groups, AMS Chelsea, Providence, 2006. (Corrected reprint of the 1976 original.)Google Scholar