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On Outer-Commutator Words

Published online by Cambridge University Press:  20 November 2018

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
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Hall, P., Finiteness conditions for soluble groups, Proc. London Math. Soc. 4 (1954), 419436.Google Scholar
2. Hall, P., The Edmonton notes on nilpotent groups, Queen Mary College Mathematics Notes, 1969 (originally published in 1957 by the Can. Math. Congress).Google Scholar
3. Rhemtulla, A. H., A problem in bounded expressibility in free products, Proc. Cambridge Philos. Soc. 64 (1968), 573584.Google Scholar
4. Rhemtulla, A. H., On commutators of certain finitely-generated soluble groups, Can. J. Math. 21 (1969), 11601164.Google Scholar
5. Robinson, Derek J. S., Finiteness conditions and generalized soluble groups, I, Ergebnisse der Mathematik, Volume 62, 119121 (Springer, Berlin, 1972).Google Scholar
6. Stroud, P. W., Thesis, Cambridge (1966).Google Scholar
7. Turner-Smith, R. F., Finiteness conditions for verbal subgroups, J. London Math. Soc. 41 (1966), 166176.Google Scholar