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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Aivazidis, S., Isaacs, I.M. Large abelian normal subgroups. Arch. Math. 111, 113–122 (2018). https://doi.org/10.1007/s00013-018-1192-y
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DOI: https://doi.org/10.1007/s00013-018-1192-y