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On Outer-Commutator Words

Published online by Cambridge University Press:  20 November 2018

Jeremy Wilson
Jeremy Wilson*
Affiliation:
University of Lancaster, Lancaster, England
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Let F be the group freely generated by the countably infinite set X = {x1, x2, . . . ,xi, . . . }. Let w(x1, x2, . . . , xn) be a reduced word representing an element of F and let G be an arbitrary group. Then V(w, G) will denote the set

whose elements will be called values of w in G. The subgroup of G generated by V(w, G) will be called the verbal subgroup of G with respect to w and be denoted by w(G).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 608 - 620
Copyright
Copyright © Canadian Mathematical Society 1974

References

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