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Dear GAP Forum:

I am interested in computing finite representations of the pure braid group

starting from Burau and Gassner representations.

For example, the Burau representation maps into the invertible matrices over

the ring of Laurent polynomials with integer coefficients,which is the group

ring of Z. A simple idea is to replace Z by Z mod n and either replace Z by a

finite cyclic group or mod out by an ideal, e.g. (t-1)^2.

I have tried the first approach by constructing the group ring R of Z/mZ with

coefficients in Z/nZ, which is straightforward in GAP. Then I consider the

ring MR of square matrices with coefficients in R of size, say 4.

It is possible to define a subset H of MR which is the image of a

representation of the pure braid group and it is a subgroup of the invertible

matrices. The problem is that GAP only recognize a monoid structure on H;

this monoid is finitely generated and the inverses of the generators can be

computed by hand. Is there an easy way to help GAP recognize the group

structure of H?

Thanks, Enrique ARTAL.

Miles-Receive-Header: reply

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