On a Group Presentation Due to Fox
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 247-248
Voir la notice de l'article provenant de la source Cambridge University Press
In 1956 R. H. Fox had occasion, while investigating fundamental groups of topological surfaces, to believe that the group <a, b | ab 2=b 3 a, ba 2=a 2 b> was trivial. Using the Todd-Coxeter coset enumeration algorithm a proof was obtained, see [3], and this algorithmic proof was used to produce an algebraic proof, see [2]. In [1] Benson and Mendelsohn, using a similar method to that of [2] showed that <a, b | ab n =b n+1 a, ba n =a n+1 b> is trivial. In this note we give a direct proof for the more general problem of describing the structure of the group <a, b | ab n =b l a, ba n =a l b>.
Campbell, C. M.; Robertson, E. F. On a Group Presentation Due to Fox. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 247-248. doi: 10.4153/CMB-1976-039-9
@article{10_4153_CMB_1976_039_9,
author = {Campbell, C. M. and Robertson, E. F.},
title = {On a {Group} {Presentation} {Due} to {Fox}},
journal = {Canadian mathematical bulletin},
pages = {247--248},
year = {1976},
volume = {19},
number = {2},
doi = {10.4153/CMB-1976-039-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-039-9/}
}
[1] 1. Benson, C. T. and Mendelsohn, N. S., A calculus for a certain class of word problems in groups, J. Combinatorial Theory 1 (1966), 202–208. Google Scholar | DOI
[2] 2. Campbell, C. M., Enumeration of cosets and solutions of some word problems in groups, Dissertation, McGill University, 1965. Google Scholar
[3] 3. Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete groups (Springer, Berlin, 2nd. edition 1965). Google Scholar
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