On certain permutation representations of the braid group

Valentin Vankov Iliev

Published 2009-10-09, updated 2009-12-08Version 2

This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the symmetric group on $n$ letters by an appropriate abelian group, and in "half" of the cases this extension splits.