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A. Ballester-Bolinches, John Cossey, Liangcai Zhang

Generalised norms in finite soluble groups

J. Algebra, 402, 392-405 (2014)

http://dx.doi.org/10.1016/j.jalgebra.2013.12.012

Abstract: We give a framework for a number of generalisations of Baer’s norm that have appeared recently. For a class C of finite nilpotent groups we define the C-norm κC(G) of a finite group G to be the intersection of the normalisers of the subgroups of G that are not in C. We show that those groups for which the C-norm is not hypercentral have a very restricted structure. The non-nilpotent groups G for which G = κC (G) 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.


MSC: 20D10, 20D20, 20D25
Keywords: Finite group, normaliser, norm