Congruence subgroups of braid groups and crystallographic quotients. Part I

Abstract

This paper is the first of a two part series devoted to describing relations between congruence and crystallographic braid groups. We recall and introduce some elements belonging to congruence braid groups and we establish some (iso)-morphisms between crystallographic braid groups and corresponding quotients of congruence braid groups.

Minor revisions; accepted by Australian Journal of Mathematics