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arXiv · 0810.4870

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

Montserrat Casals-Ruiz·Ilya Kazachkov·Vladimir Remeslennikov
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Abstract

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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Montserrat Casals-Ruiz, Ilya Kazachkov, Vladimir Remeslennikov. 2008-11-03. Elementary equivalence of right-angled Coxeter groups and graph products of finite abelian groups. https://doi.org/10.1112/blms%2Fbdp103

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