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Quotient closed metanilpotent Fitting classes

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

T. R. Berger ,
R. A. Bryce  and
John Cossey
T. R. Berger
Affiliation:
School of Mathematics University of MinnesotaMinneapolis, Minnesota 55455, U.S.A.
R. A. Bryce
Affiliation:
Department of Mathematics Faculty of Science Australian National UniversityP.O. Box 4 Canberra, A.C.T. 2601, Australia
John Cossey
Affiliation:
Department of Mathematics Faculty of Science Australian National UniversityP.O. Box 4 Canberra, A.C.T. 2601, Australia
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Abstract

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A Fitting class of finite soluble groups is one closed under the formation of normal subgroups and products of normal subgroups. It is shown that the Fitting classes of metanilpotent groups which are quotient group closed as well are primitive saturated formuations.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 157 - 163
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bryce, R. A. and Cossey, John, ‘Fitting formations of finite soluble groups’, Math. Z. 127 (1972), 217–223.CrossRefGoogle Scholar
[2]Bryce, R. A. and Cossey, John, ‘Metanilpotent Fitting classes’, J. Austral. Math. Soc. 12 (1974), 295–304.Google Scholar
[3]Bryce, R. A. and Cossey, John, ‘Subgroup closed Fitting classes are formations, Math. Proc. Cambridge Philos. Soc. 91 (1982), 225–258.Google Scholar
[4]Hawkes, T. O., ‘Skeletal classes of soluble groups’, Arch. Math. 22 (1971), 577–589.Google Scholar
[5]Neuman, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar