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A criterion for the Hall-closure of Fitting classes

Published online by Cambridge University Press:  17 April 2009

Owen J. Brison
Owen J. Brison
Affiliation:
Secção de Matemática Pura, Faculdade de Ciências, Avenida 24 de Julho, 134, 3°, 1.300 Lisboa, Portugal.
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Abstract

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In a recent paper, Cusack has given a criterion, in terms of the Fitting class “join” operation, for a normal Fitting class to be closed under the taking of Hall π-subgroups. Here we show that Cusack's result can be slightly modified so as to give a criterion for any Fitting class of finite soluble groups to be closed under taking Hall π-subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 361 - 365
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Beidleman, James C. und Hauck, Peter, “Über Fittingklassen und die Lockett-Vermutung”, Math. Z. 167 (1979), 161–167.CrossRefGoogle Scholar
[2]Blessenohl, Dieter und Gaschütz, Wolfgang, “Über normale Schunck– und Fittingklassen”, Math. Z. 118 (1970), 1–8.CrossRefGoogle Scholar
[3]Brison, Owen J., “Hall operators for Fitting classes”, Arch. Math. (Basel) 33 (1979), 1–9.CrossRefGoogle Scholar
[4]Cusack, Elspeth, “The join of two Fitting classes”, Math. Z. 167 (1979), 37–47.CrossRefGoogle Scholar
[5]Cusack, Elspeth, “Normal Fitting classes and Hall subgroups”, Bull. Austral. Math. Soc. 21 (1980), 229–236.CrossRefGoogle Scholar
[6]Lockett, F. Peter, “The Fitting class *”, Math. Z. 137 (1974), 131–136.CrossRefGoogle Scholar