On finite factorized groups with permutable subgroups of factors

Two subgroups A and B of a group  G are called msp-permutable if the following statements hold: AB  is a subgroup of  G ; the subgroups P and Q are mutually permutable, where P  is an arbitrary Sylow p -subgroup of  A and Q  is an arbitrary Sylow q -subgroup of  B , p ≠ q . In the present paper, we...

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Bibliographic Details
Published in:Archiv der Mathematik 2021-03, Vol.116 (3), p.241-249
Main Authors: Monakhov, Victor S., Trofimuk, Alexander A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
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Summary:Two subgroups A and B of a group  G are called msp-permutable if the following statements hold: AB  is a subgroup of  G ; the subgroups P and Q are mutually permutable, where P  is an arbitrary Sylow p -subgroup of  A and Q  is an arbitrary Sylow q -subgroup of  B , p ≠ q . In the present paper, we investigate groups that are factorized by two msp-permutable subgroups. In particular, the supersolubility of the product of two supersoluble msp-permutable subgroups is proved.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-020-01535-3