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FINITE GROUPS WITH SOME WEAKLY S-SUPPLEMENTED SUBGROUPS

Published online by Cambridge University Press:  08 December 2010

WENBIN GUO ,
K. P. SHUM  and
FENGYAN XIE
WENBIN GUO
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei 230026, China e-mail: wbguo@ustc.edu.cn
K. P. SHUM
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China e-mail: kpshum@maths.hku.hk
FENGYAN XIE
Affiliation:
Humanistic Management College, Anyang Normal University, Anyang 455000, China e-mail: kfxiefengyan@163.com
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Abstract

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Let H be a subgroup of a group G. Then, we call H weakly s-supplemented in G if G has a subgroup T such that HT = G and H ∩ T ≤ HsG, where HsG is the largest s-permutable subgroup of G contained in H. In this paper, we use the weakly s-supplemented subgroups to characterize the structure of groups. A series of known results in the literature are unified and generalized.

Keywords

20D1020D25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 211 - 222
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

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