Large abelian normal subgroups |
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Authors: | S Aivazidis I M Isaacs |
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Institution: | 1.Athens,Greece;2.Department of Mathematics,University of Wisconsin,Madison,USA |
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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 \(\Gamma \). |
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