Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-17T13:35:41.344Z Has data issue: false hasContentIssue false

Sub-direct product closed Fitting classes

Published online by Cambridge University Press:  17 April 2009

R.A. Bryce
Affiliation:
Department of Pure Mathematics, Australian National University, G.P.O. Box 4, CANBERRA, 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.

It is shown that in the Fitting class of all finite p-by-q groups, where p and q are different primes, there is among the sub-direct product closed sub-Fitting classes a unique maximal one: it consists of the groups whose minimal normal subgroups are central.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Berger, T.R., Bryce, R.A. and Cossey, John, “Quotient closed metanilpotent Fitting classes”, J. Austral. Math. Soc. Ser A. 38 (1985), 157163.CrossRefGoogle Scholar
[2]Bryce, R.A. and Cossey, John, “Metanilpotent Fitting classes”, J. Austral. Math. Soc. 17 (1974), 285304.CrossRefGoogle Scholar
[3]Bryce, R.A. and Cossey, John, “Subdirect product closed Fitting classes”. Proc. Second Int. conf. Theory of Groups,Australian National university, 1973. (Springer-Verlag, Berlin-Heidelbery-New York, 1974).CrossRefGoogle Scholar
[4]Bryce, R.A. and Cossey, John, “Subgroup closed Fitting classes are formations.” Math. Proc. Cambridge Philos. Soc. 91 (1982), 225258.CrossRefGoogle Scholar
[5]Hawkes, Trevor O., “On Fitting formations”, Math. Z. 117 (1970), 177182.CrossRefGoogle Scholar