  The twin group $T_n$ is a right angled Coxeter group generated by $n- 1$
involutions and having only far commutativity relations. These groups can be
thought of as planar analogues of Artin braid groups. In this note, 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 $T_n$ have $R_\infty$-property
and are not co-Hopfian for $n \ge 3$.
