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SUBGROUPS OF FINITE GROUPS WITH A STRONG COVER-AVOIDANCE PROPERTY

Published online by Cambridge University Press:  17 April 2009

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.

Type
Research Article
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), 335342.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), 161170.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), 297308.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