Elementary equivalence of right-angled Coxeter groups and graph products of finite abelian groups

Montserrat Casals-Ruiz, Ilya Kazachkov, Vladimir Remeslennikov

Published 2008-10-27, updated 2008-11-03Version 2

We show that graph products of finite abelian groups are elementarily equivalent if and only if they are $\exists\forall$-equivalent if and only if they are isomorphic. In particular, two right-angled Coxeter groups are elementarily equivalent if and only if they are isomorphic.