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On a property of verbal and marginal subgroups

Published online by Cambridge University Press:  24 October 2008

P. W. Stroud
P. W. Stroud
Affiliation:
Trinity College, Cambridge
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Extract

Let G be a group, and let φ (x1, …, xn) be any word in the variables x1, …, xn. We denote by φ(G) and φ*(G) respectively the corresponding verbal and marginal subgroups of G, which are defined as follows.

(i) φ(G)is the subgroup generated by all elements of the form φ(a1; …, an) with ai in G(for i = 1, 2, …, n);

(ii) an element b of G lies in φ*(G) if and only if

for all choices of a1, …, an in G and i= 1, 2, …,n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 41 - 48
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

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