Paper “Generalised norms in finite soluble groups” published in J. Algebra

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

A. Ballester-Bolinches, John Cossey, Liangcai Zhang

Generalised norms in finite soluble groups

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

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