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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: Adolfo.Ballester@uv.es)
LUIS M. EZQUERRO*
Affiliation:
Departamento of Matemáticas, Universidad Pública de Navarra, Campus de Arrosadía, E-31006 Pamplona, Navarra, Spain (email: ezquerro@unavarra.es)
ALEXANDER N. SKIBA
Affiliation:
Department of Mathematics, Gomel State University F. Skorina, Gomel 246019, Belarus (email: alexander.skiba49@gmail.com)
*
✉For correspondence; e-mail: ezquerro@unavarra.es
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Abstract

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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

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