Hostname: page-component-5cf477f64f-54txb Total loading time: 0 Render date: 2025-04-05T06:21:27.398Z Has data issue: false hasContentIssue false
  • English
  • Français

A Problem of R. H. Fox

Published online by Cambridge University Press:  20 November 2018

Narain Gupta
Narain Gupta*
Affiliation:
Department of Mathematics, University of Manitoba Winnipeg, Manitoba R3T 2N2
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.

The purpose of this expository article is to familiarize the reader with one of the fundamental problems in the theory of infinite groups. We give an up-to-date account of the so-called Fox problem which concerns the identification of certain normal subgroups of free groups arising out of certain ideals in the free group rings. We assume that the reader is familiar with the elementary concepts of algebra.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 129 - 136
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Birman, Joan S., Braids, links and mapping class groups, Ann. Math. Studies 82, 1974.Google Scholar
2. Enright, Dennis E., Triangular matrices over group rings, Doctoral thesis, New York University, 1968.Google Scholar
3. Fox, R. H., Free differential Calculus I — Derivations in free group rings, Ann. of Math.. 57 (1953), 547-560.Google Scholar
4. Gupta, Narain, Fox subgroups of free groups, J. Pure and Appl. Algebra. 11 (1977), 1-7.10.1016/0022-4049(77)90033-0Google Scholar
5. Gupta, C. K. and Gupta, N. D., Power series and matrix representations of certain relatively free groups, Lecture Notes in Mathematics, No 372 (Springer-Verlag, 191 A), 318-329.Google Scholar
6. Gupta, N. D., and Passi, I. B. S., Some properties of Fox subgroups of free groups, J. Algebra. 43 (1976), 198-211.10.1016/0021-8693(76)90154-XGoogle Scholar
7. Hurley, T. C., On a problem of Fox, Invent. Math.. 21 (1973), 139-141.Google Scholar
8. Magnus, W., Uber Beziehungen Zwischen Hoheren Kommutatoren, J. Reine Angew. Math.. 177 (1937), 105-115.Google Scholar
9. Magnus, W., On a theorem of Marshall Hall. Ann. of Math. Ser II. 40 (1939), 764-768.10.2307/1968892Google Scholar
10. Schumann, H. G., Ùber Modulun unà Gruppenbilder, Math. Ann.. 114 (1935), 385-413.Google Scholar
11. Smel'kin, A. L., Free polynilpotent groups, Izv. Akad. Nauk. SSSR Ser. Mat.. 28 (1964), 91-122 (English transi. Amer. Math. Soc. Transi. (2) 55 (1966), 270-304).Google Scholar
12. Ward, M. A., Basic commutators, Phil. Trans. Royal Soc. of London Ser. A,. 264 (1969), 343-412.10.1098/rsta.1969.0032Google Scholar