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arxiv: 0810.4870 · v2 · pith:ZOARBXZBnew · submitted 2008-10-27 · 🧮 math.GR · math.LO

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

Montserrat Casals-Ruiz , Ilya Kazachkov , Vladimir Remeslennikov This is my paper
classification 🧮 math.GR math.LO
keywords groupsequivalentonlytheyabeliancoxeterelementarilyfinite
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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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