Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T22:26:21.407Z Has data issue: false hasContentIssue false
  • English
  • Français

A problem of bounded expressibility in free products

Published online by Cambridge University Press:  24 October 2008

A. H. Rhemtulla
A. H. Rhemtulla
Affiliation:
University of Alberta
Get access Rights & Permissions [Opens in a new window]

Extract

1·1. The main result. Let ø = ø(x1, x2, …, xn) be a word in n variables and let G be a group. A ø-element of G is any element of the form ø(x1, x2, …, xn)±1 with xi ∈G(1 ≤ i ≤ n). The subgroup generated by all the ø-elements of G is the verbal subgroup ø(G) of G. If there is a positive integer l such that every element of ø(G) can be expressed as the product of l or fewer ø-elements of G we say that G is ø-elliptic. If there is no such integer we say that G is ø-parabolic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 573 - 584
Copyright
Copyright © Cambridge Philosophical Society 1968

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)Rhemtulla, A. H. Thesis (Cambridge12 1966).Google Scholar
(2)Stroud, P. Thesis (Cambridge, 1966).Google Scholar
(3)Griffiths, H. B.A note on commutators in free products. Proc. Cambridge Philos. Soc. 50 (1954), 178–188.CrossRefGoogle Scholar
(4)Ito, N.A theorem on alternating group An(n ≥ 5). Math. Japon. 2 (1951), 59–60.Google Scholar
(5)Thompson, R. C.Commutators in the special and general linear groups. Tran. Amer. Math. Soc. 101 (1961), 16–33.CrossRefGoogle Scholar