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), 21972204
MSC (2000):
Primary 20D10, 20D20
Published electronically:
March 24, 2004
MathSciNet review:
2052394
Fulltext PDF Free Access
Abstract 
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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:
http://dx.doi.org/10.1090/S000299390407296X
PII:
S 00029939(04)07296X
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
