Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-25T17:13:53.986Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
K. P. Shum
Affiliation:
Faculty of ScienceThe Chinese Universityof Hong Kong Shatin, N.T. P. R. of China (S AR) e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

[1]Arad, Z. and Fisman, E., ‘On finite factorizable groups’, J. Algebra 86 (1984), 522–548.Google Scholar
[2]Asaad, M., Ballester-Bolinches, A. and Pedraza-Aguilera, M. C., ‘A note on minimal subgroups of finite groups’, Comm. Algebra 24 (1996), 2771–2776.CrossRefGoogle Scholar
[3]Ballester-Bolinches, A., ‘ℋ-normalizers and local definitions of saturated formations of finite groups’, Israel J. Math. 67 (1989), 312–326.CrossRefGoogle Scholar
[4]Ballester-Bolinches, A., Wang, Yanming and Guo, Xiuyun, ‘c–supplemented subgroups of finite groups’, Glasgow Math. J. 42 (2000), 383–389.CrossRefGoogle Scholar
[5]Buckley, J., ‘Finite groups whose minimal subgroups are normal’, Math. Z. 116 (1970), 15–17.CrossRefGoogle Scholar
[6]Doerk, K. and Hawkes, T., Finite solvable groups (Walter de Gruyter, Berlin, 1992).CrossRefGoogle Scholar
[7]Dornhoff, L., ‘M-groups and 2-groups’, Math. Z. 100 (1967), 226–256.CrossRefGoogle Scholar
[8]Feit, W. and Thompson, J. G., ‘Solvability of groups of odd order’, Pacific J. Math. 13 (1963), 775–1029.Google Scholar
[9]Gross, F., ‘Conjugacy of odd order Hall subgroups’, Bull. London Math. Soc. 19 (1987), 311–319.CrossRefGoogle Scholar
[10]Li, Deyu and Guo, Xiuyun, ‘The influence of c-normality of subgroups on the structure of finite groups (II)’, Comm. Algebra 26 (1998), 1913–1922.Google Scholar
[11]Li, Deyu and Guo, Xiuyun, ‘The influence of c–normality of subgroups on the structure of finite groups’, J. Pure Appl. Algebra 150 (2000), 53–60.Google Scholar
[12]Robinson, D. J. S., A course in the theory of groups (Springer, New York, 1993).Google Scholar
[13]Srinivassan, S., ‘Two sufficient conditions for supersolvability of finite groups’, Israel J. Math. 35 (1980), 210–214.CrossRefGoogle Scholar
[14]Wall, G. ‘Groups with maximal subgroups of Sylow subgroups normal’, Israel J. Math. 43 (1982), 166–168.Google Scholar