Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T13:57:47.832Z Has data issue: false hasContentIssue false

Minimal verbal subgroups

Published online by Cambridge University Press:  24 October 2008

L. G. Kovács
Affiliation:
Australian National University
M. F. Newman
Affiliation:
Australian National University

Extract

Introduction. In this note we obtain a description of the structure of the minimal verbal subgroups of a finite group which has, among others, the following consequences:

Theorem 1. A finite group which belongs to the variety generated by its proper subgroups and proper factor-groups belongs either to the variety generated by its proper subgroups or to the variety generated by its proper factor-groups.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baer, R.Group elements of prime power index. Trans. Amer. Math. Soc. 75 (1953), 2047.CrossRefGoogle Scholar
(2)Higman, G.Some remarks on varieties of groups. Quart. J. Math. Oxford Ser. (2), 10 (1959), 165178.CrossRefGoogle Scholar
(3)Kovács, L. G. and Newman, M. F.Cross varieties of groups. Proc. Roy. Soc. Ser. A (1966) (to appear).Google Scholar
(4)Weichsel, P. M.On critical p-groups. Proc. London Math. Soc. (3) 14 (1964), 83100.CrossRefGoogle Scholar