Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T19:53:38.387Z Has data issue: false hasContentIssue false

Quotient closed metanilpotent Fitting classes

Published online by Cambridge University Press:  09 April 2009

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bryce, R. A. and Cossey, John, ‘Fitting formations of finite soluble groups’, Math. Z. 127 (1972), 217223.CrossRefGoogle Scholar
[2]Bryce, R. A. and Cossey, John, ‘Metanilpotent Fitting classes’, J. Austral. Math. Soc. 12 (1974), 295304.Google Scholar
[3]Bryce, R. A. and Cossey, John, ‘Subgroup closed Fitting classes are formations, Math. Proc. Cambridge Philos. Soc. 91 (1982), 225258.Google Scholar
[4]Hawkes, T. O., ‘Skeletal classes of soluble groups’, Arch. Math. 22 (1971), 577589.Google Scholar
[5]Neuman, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar