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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On $c$-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups


Authors: Huaquan Wei, Yanming Wang and Yangming Li
Journal: Proc. Amer. Math. Soc. 132 (2004), 2197-2204
MSC (2000): Primary 20D10, 20D20
Published electronically: March 24, 2004
MathSciNet review: 2052394
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper proves: Let ${\cal F}$ be a saturated formation containing ${\cal U}$. Suppose that $G$ is a group with a normal subgroup $H$ such that $G/H \in {\cal F}$.

(1) If all maximal subgroups of any Sylow subgroup of $F^*(H)$ are $c$-supple- mented in $G$, then $G \in {\cal F}$;

(2) If all minimal subgroups and all cyclic subgroups with order 4 of $F^*(H)$ are $c$-supplemented in $G$, then $G \in {\cal F}$.


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Additional Information

Huaquan Wei
Affiliation: Department of Mathematics, Zhongshan University, Guangzhou 510275, China and Department of Mathematics, Guangxi Teacher’s College, Nanning, 530001, China
Email: weihuaquan@163.com

Yanming Wang
Affiliation: Lingnan College and Department of Mathematics, Zhongshan University, Guangzhou, 510275, China
Email: stswym@zsu.edu.cn

Yangming Li
Affiliation: Department of Mathematics, Guangdong College of Education, Guangzhou, 510310, China
Email: liyangming@gdei.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07296-X
PII: S 0002-9939(04)07296-X
Keywords: $c$-supplemented subgroup, supersolvable group, the generalized Fitting subgroup, saturated formation
Received by editor(s): October 21, 2002
Received by editor(s) in revised form: February 16, 2003
Published electronically: March 24, 2004
Additional Notes: Project supported in part by NSF of China, NSF of Guangdong, Fund from Education Ministry of China and ARC of ZSU
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2004 American Mathematical Society



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