Some remarks on twin groups

Abstract

The twin group [Formula: see text] is a right angled Coxeter group generated by [Formula: see text] involutions and having only far commutativity relations. These groups can be thought of as planar analogues of Artin braid groups. In this paper, we study some properties of twin groups whose analogues are well known for Artin braid groups. We give an algorithm for two twins to be equivalent under individual Markov moves. Further, we show that twin groups [Formula: see text] have [Formula: see text]-property and are not co-Hopfian for [Formula: see text].