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The Jordan-Hölder theorem and prefrattini subgroups of finite groups

Published online by Cambridge University Press:  18 May 2009

A. Ballester-Bolinches  and
L. M. Ezquerro
A. Ballester-Bolinches
Affiliation:
Departament D'Àlgebra, Universitat de València, C/Dr. Moliner 50, 46100 Burjassot (València), Spain.
L. M. Ezquerro
Affiliation:
Departamento de Mátematica E Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain.
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All groups considered are finite. In recent years a number of generalizations of the classic Jordan-Hölder Theorem have been obtained (see [7], Theorem A.9.13): in a finite group G a one-to-one correspondence as in the Jordan-Holder Theorem can be defined preserving not only G-isomorphic chief factors but even their property of being Frattini or non-Frattini chief factors. In [2] and [13] a new direction of generalization is presented: the above correspondence can be defined in such a way that the corresponding non-Frattini chief factors have the same complement (supplement).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 265 - 277
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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