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Permutability in finite soluble groups

Published online by Cambridge University Press:  24 October 2008

A. Ballester-Bolinches  and
M. D. Pérez-Ramos
A. Ballester-Bolinches
Affiliation:
Departament d'Algebra, Universitat de València
M. D. Pérez-Ramos
Affiliation:
c/Dr Moliner 50, 46100 Burjassot (València), Spain
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Extract

Let G be a finite soluble group and let Σ be a Hall system of G. A subgroup U of G is said to be Σ-permutable if U permutes with every member of Σ. In [1; I, 4·29] it is proved that if U and V are Σ-permutable subgroups of G then so also are U ∩ V and 〈U, V〉.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 3 , May 1994 , pp. 393 - 396
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Doerk, K. and Hawkes, T.. Finite soluble groups (Walter de Gruyter, 1992).CrossRefGoogle Scholar
[2]Doerk, K.. Eine Bemerkung über das Reduzieren von Hallgruppen in endlichen auflösbaren Gruppen, Arch. Math. 60 (1993), 505–507.CrossRefGoogle Scholar