Finite Groups with Three Given Subgroups

Given a hereditary saturated formation F of soluble groups, we study finite groups with three F-subgroups of coprime indices. We obtain the new criteria for these groups to lie in the Shemetkov formations, the formations of all supersoluble groups, the formations of all groups with nilpotent commuta...

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Bibliographic Details
Published in:	Siberian mathematical journal Vol. 59; no. 1; pp. 50 - 58
Main Authors:	Vasil’ev, A. F., Vasil’eva, T. I., Parfenkov, K. L.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 2018 Springer Nature B.V
Subjects:	Formations Mathematics Mathematics and Statistics Subgroups w-supersoluble group supersoluble group finite group formation hereditary saturated formation F-subnormal subgroup
Online Access:	Get full text
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Summary:	Given a hereditary saturated formation F of soluble groups, we study finite groups with three F-subgroups of coprime indices. We obtain the new criteria for these groups to lie in the Shemetkov formations, the formations of all supersoluble groups, the formations of all groups with nilpotent commutator subgroup, and other formations.
ISSN:	0037-4466 1573-9260
DOI:	10.1134/S0037446618010068