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ON CONJUGACY OF SUPPLEMENTS OF NORMAL SUBGROUPS OF FINITE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  13 June 2013

A. BALLESTER-BOLINCHES  and
LUIS M. EZQUERRO
A. BALLESTER-BOLINCHES*
Affiliation:
Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot, València, Spain
LUIS M. EZQUERRO
Affiliation:
Departamento of Matemáticas, Universidad Pública de Navarra, Campus de Arro-sadía, E-31006 Pamplona, Navarra, Spain email ezquerro@unavarra.es
*
✉Adolfo.Ballester@uv.es
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Abstract

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The objective of this paper is to find some sufficient conditions to ensure the conjugacy of supplements of a normal subgroup of a soluble group.

Keywords

finite groupssupplementsSchunck classesformations

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
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 293 - 299
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Ballester-Bolinches, A. and Ezquerro, L. M., Classes of Finite Groups (Springer, Dordrecht, 2006).Google Scholar
Ballester-Bolinches, A. and Pérez-Ramos, M. D., ‘On $\mathfrak{F}$-subnormal subgroups and Frattini-like subgroups of a finite group’, Glasgow Math. J. 36 (1994), 241–247.CrossRefGoogle Scholar
Doerk, K. and Hawkes, T., Finite Soluble Groups (Walter de Gruyter, Berlin, 1992).CrossRefGoogle Scholar
Parker, C. and Rowley, P., ‘A note on conjugacy of supplements in finite soluble groups’, Bull. Lond. Math. Soc. 42 (2010), 417–419.Google Scholar
Weiss, E., Cohomology of Groups (Academic Press, New York, 1969).Google Scholar