6533b836fe1ef96bd12a1bd8
RESEARCH PRODUCT
Generalised norms in finite soluble groups
John CosseyLiangcai ZhangAdolfo Ballester-bolinchessubject
CombinatoricsMathematics::Group TheoryNilpotentFinite groupAlgebra and Number TheoryCoprime integersNorm (group)Structure (category theory)Order (group theory)Nilpotent groupQuotientMathematicsdescription
Abstract We give a framework for a number of generalisations of Baerʼs norm that have appeared recently. For a class C of finite nilpotent groups we define the C -norm κ C ( 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 = κ C ( 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-03-01 | Journal of Algebra |