Conditional permutability of subgroups and certain classes of groups

Conditional permutability of subgroups and certain classes of groups

Two subgroups A and B of a finite group G are said to be tcc-permutable if X permutes with Yg for some g∈〈X,Y〉, for all X≤A and all Y≤B. Some aspects about the normal structure of a product of two tcc-permutable subgroups are analyzed. The obtained results allow to study the behaviour of such produc...

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Bibliographic Details
Published in:Journal of algebra Vol. 476; pp. 395 - 414
Main Authors: Arroyo-Jordá, M., Arroyo-Jordá, P.
Format: Journal Article
Language:English
Published: Elsevier Inc 15-04-2017
Subjects:
Classes of groups
Conditional permutability
Finite groups
Products of subgroups
20D10
20D20
Conditional permutability
20D40
Finite groups
Products of subgroups
Classes of groups
20D35
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Summary:Two subgroups A and B of a finite group G are said to be tcc-permutable if X permutes with Yg for some g∈〈X,Y〉, for all X≤A and all Y≤B. Some aspects about the normal structure of a product of two tcc-permutable subgroups are analyzed. The obtained results allow to study the behaviour of such products in relation with certain classes of groups, namely the class of T-groups and some generalizations.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2016.12.020