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Sibirsk. Mat. Zh., 2016, Volume 57, Number 3, Pages 603–616 (Mi smj2766)  

Finite widely $c$-supersoluble groups and their mutually permutable products

A. F. Vasil'eva, T. I. Vasil'evab, E. N. Myslovetsa

a Francisk Skorina Gomel State University, Gomel, Belarus
b Belarusian State University of Transport, Gomel, Belarus

Abstract: 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.

Keywords: finite group, $c$-supersoluble group, $w$-supersoluble group, widely $c$-supersoluble group, composition formation, product of mutually permutable subgroups.

DOI: https://doi.org/10.17377/smzh.2016.57.308

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English version:
Siberian Mathematical Journal, 2016, 57:3, 476–485

Bibliographic databases:

Document Type: Article
UDC: 512.542
Received: 18.05.2015

Citation: A. F. Vasil'ev, T. I. Vasil'eva, E. N. Myslovets, “Finite widely $c$-supersoluble groups and their mutually permutable products”, Sibirsk. Mat. Zh., 57:3 (2016), 603–616; Siberian Math. J., 57:3 (2016), 476–485

Citation in format AMSBIB
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\paper Finite widely $c$-supersoluble groups and their mutually permutable products
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 3
\pages 603--616
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