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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
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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

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References

REFERENCES

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