COMMENSURATORS OF RIGHT-ANGLED ARTIN GROUPS AND MAPPING CLASS GROUPS MATT CLAY, CHRISTOPHER J. LEININGER, AND DAN MARGALIT Abstract. We prove that, aside from the obvious exceptions, the mapping class We prove that, aside from the obvious exceptions, the mapping class group of a compact orientable surface is not abstractly commensurable with any right-angled Artin group. Our argument applies to...

The Artin exponent induced from cyclic subgroups of finite groups was studied extensively by T.Y. Lam in [5]. A Burnside ring theoretic version of the results in [5] for p-groups was given in [6]. Here we shall be interested in looking at the Artin exponent induced from the elementary abelian subgroups of finite p-groups using some results of A. Dress in [3].

In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Also we show that right-angled Artin groups are residually torsion-free nilpotent. Moreover, we investigate the profinite topology of F2 × F2 and of the group L in [18], which are the only obstructions for the subgroup separab...