Generalised norms in finite soluble groups

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• 作者：Adolfo Ballester-Bolinches ; John Cossey ; Liangcai Zhang
• 关键词：20D10 ; 20D20 ; 20D25
• 刊名：Journal of Algebra
• 出版年：15 March, 2014
• 年：2014
• 卷：402
• 期：Complete
• 页码：392-405
• 全文大小：289 K

文摘

We give a framework for a number of generalisations of Baer始s norm that have appeared recently. For a class of finite nilpotent groups we define the -norm of a finite group G to be the intersection of the normalisers of the subgroups of G that are not in . We show that those groups for which the -norm is not hypercentral have a very restricted structure. The non-nilpotent groups G for which have been classified for some classes. We give a classification for nilpotent classes closed under subgroups, quotients and direct products of groups of coprime order and show the known classifications can be deduced from our classification.