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

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

2008-10-27

arxiv.org/abs/0810.4870v2

Mathematics

Group Theory

7 pages; version 2: added a reference to David Radcliffe's rigidity result and Remark 2.4

Scientific paper

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.

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