On a property of verbal and marginal subgroups
Published online by Cambridge University Press: 24 October 2008
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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