Finite widely c-supersoluble groups and their mutually permutable products

A group is c-supersoluble if all its chief factors are isomorphic to simple groups. We introduce the notion of widely c -supersoluble group, which generalizes c -supersolubility. We obtain the properties and find applications of products of mutually permutable subgroups. In particular, we establish...

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Bibliographic Details
Published in:	Siberian mathematical journal Vol. 57; no. 3; pp. 476 - 485
Main Authors:	Vasil’ev, A. F., Vasil’eva, T. I., Myslovets, E. N.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-05-2016
Subjects:	Mathematics Mathematics and Statistics w-supersoluble group supersoluble group finite group composition formation product of mutually permutable subgroups widely
Online Access:	Get full text
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Summary:	A group is c-supersoluble if all its chief factors are isomorphic to simple groups. We introduce the notion of widely c -supersoluble group, which generalizes c -supersolubility. We obtain the properties and find applications of products of mutually permutable subgroups. In particular, we establish the wide c-supersolubility of a finite group that is a product of two mutually permutable c-supersoluble subgroups of coprime indices.
ISSN:	0037-4466 1573-9260
DOI:	10.1134/S0037446616030083