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Closure operations for Schunck classes and formations of finite solvable groups

Published online by Cambridge University Press:  24 October 2008

Peter Forster
Affiliation:
Johannes Gutenberg-Universität, D-6500 Mainz, Germany

Extract

The purpose of the present note is to investigate the closure operations common to both the operations of forming classes and formations. Furthermore, new descriptions of formations and saturated formations in terms of closure operations are given.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)D'Arcy, P.On formations of finite groups. Arch. Math. 25 (1974), 37.CrossRefGoogle Scholar
(2)Bryant, R. M., Bryce, R. A. and Hartley, B.The formation generated by a finite group. Bull. Austral. Math. Soc. 2 (1970), 347357.CrossRefGoogle Scholar
(3)Carter, R. W., Fischer, B. and Hawkes, T. O.Extreme classes of finite soluble groups. J. Algebra 9 (1968), 285313.CrossRefGoogle Scholar
(4)Cossey, J. and MacDonald, S. O.On the definition of saturated formations of groups. Bull. Austral. Math. Soc. 4 (1971), 915.CrossRefGoogle Scholar
(5)Förster, P. Charakterisierungen einiger Schunckklassen endlicher auflösbarer Gruppen II. Math. Z. (in the Press).Google Scholar
(6)Hawkes, T. O.Closure operations for Schunck classes. J. Austral. Math. Soc. 16 (1973), 316318.CrossRefGoogle Scholar
(7)Huppert, B.Endliche Gruppen I (Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
(8)Kattwinkel, U.Die grösste untergruppenabgeschlossene Teilklasse einer Schunckklasse endlicher auflösbarer Gruppen. Arch. Math. 29 (1977), 337343.CrossRefGoogle Scholar