Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T12:23:43.414Z Has data issue: false hasContentIssue false
  • English
  • Français

On Outer-Commutator Words

Published online by Cambridge University Press:  20 November 2018

Jeremy Wilson
Jeremy Wilson*
Affiliation:
University of Lancaster, Lancaster, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let F be the group freely generated by the countably infinite set X = {x 1, x 2, . . . ,x i, . . . }. Let w(x 1, x 2, . . . , 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).

Information

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

References

1. Hall, P., Finiteness conditions for soluble groups, Proc. London Math. Soc. 4 (1954), 419–436.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), 573–584.Google Scholar
4. Rhemtulla, A. H., On commutators of certain finitely-generated soluble groups, Can. J. Math. 21 (1969), 1160–1164.Google Scholar
5. Robinson, Derek J. S., Finiteness conditions and generalized soluble groups, I, Ergebnisse der Mathematik, Volume 62, 119–121 (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), 166–176.Google Scholar