Supersolubility of a Finite Group with Normally Embedded Maximal Subgroups in Sylow Subgroups

Let P be a subgroup of a Sylow subgroup of a finite group G . If P is a Sylow subgroup of some normal subgroup of G then P is called normally embedded in G . We establish tests for a finite group G to be p -supersoluble provided that every maximal subgroup of a Sylow p -subgroup of X is normally emb...

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Bibliographic Details
Published in:Siberian mathematical journal 2018-09, Vol.59 (5), p.922-930
Main Authors: Monakhov, V. S., Trofimuk, A. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
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Summary:Let P be a subgroup of a Sylow subgroup of a finite group G . If P is a Sylow subgroup of some normal subgroup of G then P is called normally embedded in G . We establish tests for a finite group G to be p -supersoluble provided that every maximal subgroup of a Sylow p -subgroup of X is normally embedded in G. We study the cases when X is a normal subgroup of G , X = O p',p ( H ), and X = F *( H ) where H is a normal subgroup of G .
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446618050166