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arXiv · 2309.06144

Conjugacy Class Growth in Virtually Abelian Groups

Aram Dermenjian·Alex Evetts
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Abstract

We study the conjugacy class growth function in finitely generated virtually abelian groups. That is, the number of elements in the ball of radius $n$ in the Cayley graph which intersect a fixed conjugacy class. In the class of virtually abelian groups, we prove that this function is always asymptotically equivalent to a polynomial. Furthermore, we show that in any affine Coxeter group, the degree of polynomial growth of a conjugacy class is equivalent to the reflection length of any element of that class.

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Aram Dermenjian, Alex Evetts. 2023-09-12. Conjugacy Class Growth in Virtually Abelian Groups. https://doi.org/10.46298/jgcc.2025.17.1.13459

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