Aram Dermenjian ; Alex Evetts - Conjugacy Class Growth in Virtually Abelian Groups

gcc:13459 - journal of Groups, complexity, cryptology, February 24, 2025, Volume 17, Issue 1 - https://doi.org/10.46298/jgcc.2025.17.1.13459
Conjugacy Class Growth in Virtually Abelian GroupsArticle

Authors: Aram Dermenjian ; Alex Evetts

    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.


    Volume: Volume 17, Issue 1
    Published on: February 24, 2025
    Accepted on: February 20, 2025
    Submitted on: April 24, 2024
    Keywords: Mathematics - Group Theory,Mathematics - Combinatorics,05E16, 20E45, 20F55, 20F69

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