Finite groups with S-quasinormally embedded or SS-quasinormal subgroups

Suppose that G is a finite group and H is a subgroup of  G . H is said to be S -quasinormally embedded in  G if for each prime p dividing the order of  H , a Sylow p -subgroup of  H is also a Sylow p -subgroup of some S -quasinormal subgroup of  G ; H is said to be an SS -quasinormal subgroup of  G...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2014-04, Vol.142 (2), p.459-467
Main Author: Kong, Qingjun
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Suppose that G is a finite group and H is a subgroup of  G . H is said to be S -quasinormally embedded in  G if for each prime p dividing the order of  H , a Sylow p -subgroup of  H is also a Sylow p -subgroup of some S -quasinormal subgroup of  G ; H is said to be an SS -quasinormal subgroup of  G if there is a subgroup  B of  G such that G = HB and H permutes with every Sylow subgroup of  B . We fix in every non-cyclic Sylow subgroup  P of  G some subgroup  D satisfying 1
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-013-0368-y