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Weakly s-supplementally embedded minimal subgroups of finite groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  17 August 2011

Tao Zhao ,
Xianhua Li  and
Yong Xu
Tao Zhao
Affiliation:
School of Mathematical Science, Soochow University, Suzhou, Jiangsu 215006, People's Republic of China ([email protected])
Xianhua Li
Affiliation:
School of Mathematical Science, Soochow University, Suzhou, Jiangsu 215006, People's Republic of China ([email protected])
Yong Xu
Affiliation:
School of Mathematical Science, Soochow University, Suzhou, Jiangsu 215006, People's Republic of China ([email protected])
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Abstract

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Suppose that G is a finite group and H is a subgroup of G. We call H a weakly s-supplementally embedded subgroup of G if there exist a subgroup T of G and an s-quasinormally embedded subgroup Hse of G contained in H such that G = HT and H ∩ T ≤ Hse. We investigate the influence of the weakly s-supplementally embedded property of some minimal subgroups on the structure of finite groups. As an application of our results, some earlier results are generalized.

Keywords

weakly s-supplementally embedded subgroupsupersolvable groupnilpotent group

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 799 - 807
Copyright
Copyright © Edinburgh Mathematical Society 2011

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