Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T05:29:07.768Z Has data issue: false hasContentIssue false
  • English
  • Français

SUBGROUPS OF FINITE GROUPS WITH A STRONG COVER-AVOIDANCE PROPERTY

Part of: Representation theory of groups

Published online by Cambridge University Press:  17 April 2009

A. BALLESTER-BOLINCHES ,
LUIS M. EZQUERRO  and
ALEXANDER N. SKIBA
A. BALLESTER-BOLINCHES
Affiliation:
Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot, València, Spain (email: [email protected])
LUIS M. EZQUERRO*
Affiliation:
Departamento of Matemáticas, Universidad Pública de Navarra, Campus de Arrosadía, E-31006 Pamplona, Navarra, Spain (email: [email protected])
ALEXANDER N. SKIBA
Affiliation:
Department of Mathematics, Gomel State University F. Skorina, Gomel 246019, Belarus (email: [email protected])
*
✉For correspondence; 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 A of a group G has the strong cover-avoidance property in G, or A is a strong CAP-subgroup of G, if A either covers or avoids every chief factor of every subgroup of G containing A. The main aim of the present paper is to analyse the impact of the strong cover and avoidance property of the members of some relevant families of subgroups on the structure of a group.

Keywords

finite groupcover-avoidance propertysaturated formation

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D15: Nilpotent groups, $p$-groups 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 499 - 506
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The research of the first author is supported by Proyecto MTM2007-68010-C03-02, Ministerio de Educación y Ciencia de España. The research of the second author is supported by Proyecto MTM2007-68010-C03-01, Ministerio de Educación y Ciencia de España.

References

[1] Ballester-Bolinches, A. and Ezquerro, L. M., Classes of Finite Groups (Springer, Dordrecht, 2006).Google Scholar
[2] Ballester-Bolinches, A., Ezquerro, L. M. and Skiba, A. N., On second maximal subgroups of Sylow subgroups of finite groups, submitted.Google Scholar
[3] Ballester-Bolinches, A. and Pedraza-Aguilera, M. C., ‘On minimal subgroups of finite groups’, Acta Math. Hungar. 73(4) (1996), 335–342.CrossRefGoogle Scholar
[4] Doerk, K. and Hawkes, T., Finite Soluble Groups (Walter de Gruyter, Berlin, 1992).CrossRefGoogle Scholar
[5] Ezquerro, L. M., ‘A contribution to the theory of finite supersolvable groups’, Rend. Sem. Mat. Univ. Padova 89 (1993), 161–170.Google Scholar
[6] Gorenstein, D., Finite Groups (Harper & Row, New York, 1968).Google Scholar
[7] Guo, X. and Shum, K. P., ‘Cover-avoidance properties and the structure of finite groups’, J. Pure Appl. Algebra 181 (2003), 297–308.Google Scholar
[8] Huppert, B., Endliche Gruppen I, Grundlehren der Mathematischen Wissenschaften, 134 (Springer, Berlin, 1967).CrossRefGoogle Scholar
[9] Huppert, B. and Blackburn, N., Finite Groups III, Grundlehren der Mathematischen Wissenschaften, 243 (Springer, Berlin, 1982).CrossRefGoogle Scholar