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On generalized braid groups

Published online by Cambridge University Press:  18 May 2009

A. K. Napthine  and
Stephen J. Pride
A. K. Napthine
Affiliation:
Minster School, Nottingham Road, Southwell NG25 OMG University of Glasgow, Department of Mathematics, University Gardens, Glasgow, G12 8QW
Stephen J. Pride
Affiliation:
Minster School, Nottingham Road, Southwell NG25 OMG University of Glasgow, Department of Mathematics, University Gardens, Glasgow, G12 8QW
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Braid groups were introduced by Artin [1]. These groups have been studied extensively—see [2], [9] and the references cited there. Recently work has been done on “circular” braid groups and other “braid-like” groups [7], [10]. In this paper we formulate the concept of a generalized braid group, and we begin a study of the structure of such groups. In particular for such a group G1, there is a homomorphism from G onto the infinite cyclic group, the kernel of which is the derived group G1 of G. We study G1. Our results generalize results of Gorin and Lin [5], who considered the case when G is a classical braid group B(n ≥ 3). They showed that is free abelian of rank 2 if n = 3, 4 and is trivial if n ≥ 5. They also showed that is finitely presented.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 199 - 209
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

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