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On 𝓕-subnormal subgroups and Frattini-like subgroups of a finite group

Published online by Cambridge University Press:  18 May 2009

A. Ballester-Bolinches  and
M. D. PĂ©rez-Ramos
A. Ballester-Bolinches
Affiliation:
Departament D'Algebra, Universitat de Valencia, C/Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
M. D. PĂ©rez-Ramos
Affiliation:
Departament D'Algebra, Universitat de Valencia, C/Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
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Throughout the paper we consider only finite groups.

J. C. Beidleman and H. Smith [3] have proposed the following question: “If G is a group and Ha subnormal subgroup of G containing Ω(G), the Frattini subgroup of G, such that H/Ω(G)is supersoluble, is H necessarily supersoluble? “In this paper, we give not only an affirmative answer to this question but also we see that the above result still holds if supersoluble is replaced by any saturated formation containing the class of all nilpotent groups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 2 , May 1994 , pp. 241 - 247
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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