Elementary equivalence of right-angled Coxeter groups and graph products   of finite abelian groups
  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. 
Montserrat Casals-Ruiz, Ilya Kazachkov and Vladimir Remeslennikov