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Fitting classes and lattice formations I

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

M. Arroyo-Jordá  and
M. D. Pérez-Ramos
M. Arroyo-Jordá
Affiliation:
Departamento de Matemática AplicadaUniversidad Politécnica de ValenciaCamino de Vera, s/n46071 Valencia, Spain, e-mail: marroyo @mat.upv.es
M. D. Pérez-Ramos
Affiliation:
Departamento d'ÀlgebraUniversitat de València, Doctor Moliner 5046100 Burjassot (València), Spain, e-mail: dolores.perez@uv.es
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Abstract

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A lattice formation is a class of groups whose elements are the direct product of Hall subgroups corresponding to pairwise disjoint sets of primes. In this paper Fitting classes with stronger closure properties involving F-subnormal subgroups, for a lattice formation F of full characteristic, are studied. For a subgroup-closed saturated formation G, a characterisation of the G-projectors of finite soluble groups is also obtained. It is inspired by the characterisation of the Carter subgroups as the N-projectors, N being the class of nilpotent groups.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 93 - 108
Copyright
Copyright © Australian Mathematical Society 2004

References

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