On -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

DOI:
https://doi.org/10.1090/S0002-9939-04-07296-X

Published electronically:
March 24, 2004

MathSciNet review:
2052394

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper proves: Let be a saturated formation containing . Suppose that is a group with a normal subgroup such that .

(1) If all maximal subgroups of any Sylow subgroup of are -supple- mented in , then ;

(2) If all minimal subgroups and all cyclic subgroups with order 4 of are -supplemented in , then .

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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:
https://doi.org/10.1090/S0002-9939-04-07296-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