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Finite p–nilpotent groups with some subgroups c–supplemented

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Xiuyun Guo  and
K. P. Shum
Xiuyun Guo
Affiliation:
Department of MathematicsShanghai UniversityShanghai 200444 P. R. ofChina e-mail: xyguo@staff.shu.edu.cn
K. P. Shum
Affiliation:
Faculty of ScienceThe Chinese Universityof Hong Kong Shatin, N.T. P. R. of China (S AR) e-mail: kpshum@math.cuhk.edu.hk
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Abstract

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A subgroup H of a finite group G is said to be c–supplemented in G if there exists a subgroup K of G such that G = HK and H∩K is contained in coreG (H). In this paper some results for finite p–nilpotent groups are given based on some subgroups of Pc–supplemented in G, where p is a prime factor of the order of G and P is a Sylow p–subgroup of G. We also give some applications of these results.

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
Journal of the Australian Mathematical Society , Volume 78 , Issue 3 , June 2005 , pp. 429 - 439
Copyright
Copyright © Australian Mathematical Society 2005

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