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Nilpotent-like fitting formations of finite soluble groups

Published online by Cambridge University Press:  17 April 2009

A. Ballester-Bolinches ,
M. D. Pérez-Ramos  and
A. Martínez- Pastor
A. Ballester-Bolinches
Affiliation:
Department d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain
M. D. Pérez-Ramos
Affiliation:
Escuela Universitaria de Informática, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera, S/n, 46071 Valencia, Spain
A. Martínez- Pastor
Affiliation:
Department d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain
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Abstract

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Dedicated to Professor K. Doerk on his 60th Birthday.

In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 427 - 433
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Amberg, B., Franciosi, S. and de Giovanni, F., Products of Groups (Clarendon Press, Oxford, 1992).Google Scholar
[2]Ballester-Bolinches, A., Doerk, K. and Pérez-Ramos, M.D., ‘On the lattice of ℱ-subnormal subgroups’, J. Algebra 148 (1992), 42–52.Google Scholar
[3]Ballester-Bolinches, A., Martínez-Pastor, A. and Pedraza-Aguilera, M.C., ‘Finite trifactorized groups and formations’, J. Algebra 226 (2000), 990–1000.Google Scholar
[4]Ballester-Bolinches, A., Pedraza-Aguilera, M.C. and Pérez-Ramos, M.D., ‘On ℱ-subnormal; subgroups and ℱ-residuals of finite soluble groups’, J. Algebra 186 (1996), 314–322.Google Scholar
[5]Doerk, K. and Hawkes, T., Finite soluble groups (Walter De Gruyter, Berlin, New York, 1992).Google Scholar