The Group Isomorphism problem consists in deciding whether two input groups $G_1$ and $G_2$ given by their multiplication tables are isomorphic. We first give a 2-round Arthur-Merlin protocol for the Group Non-Isomorphism problem such that on input groups $(G_1,G_2)$ of size $n$, Arthur uses $O(\log^6 n)$ random bits and Merlin ... more >>>