Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T02:18:08.784Z Has data issue: false hasContentIssue false

Generator conditions on the fitting subgroup of a polycyclic group

Published online by Cambridge University Press:  20 January 2009

J. F. Humphreys
Affiliation:
Department of Pure Mathematics, The University, Liverpool.
Rights & Permissions [Opens in a new window]

Extract

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.

In an earlier paper (3), polycyclic groups in which every subgroup can be generated by d, or fewer, elements were studied. In this paper we investigate the structure of those polycyclic groups G such that every abelian normal subgroup of F(G), the Fitting subgroup of G, can begenerated by at most d elements.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

(1) Frick, M. and Newman, M. F., Soluble linear groups, Bull. Austral. Math. Soc. 6 (1972), 3144.CrossRefGoogle Scholar
(2) Hall, P., The Frattini subgroups of finitely generated groups, Proc. London Math. Soc. 11 (1961), 327352.CrossRefGoogle Scholar
(3) Humphreys, J. F. and McCutcheon, J. J., A bound for the derived length of certain polycyclic groups, J. London Math. Soc. 3 (1971), 463468.CrossRefGoogle Scholar
(4) Huppert, B., Lineare auflosbare Gruppen, Math. Z. 67 (1957), 479518.CrossRefGoogle Scholar
(5) Robinson, D. J. S., Finiteness conditions and generalised soluble groups (Springer-Verlag, Berlin, 1972).Google Scholar
(6) Suprunenko, D. A., Soluble and nilpotent linear groups, Transl. Math. Monographs Vol. 9. Amer. Math. Soc, Providence 1963.Google Scholar