2016/10/25 by Valentin Mercier, Mercier, Valentin · 1 citation
Computer Science · Mathematics · #05E18 #20E22 #20E45 #20F65 #20F69 #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1610.07868
openalex publication_date 2016/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider groups of the form G\wr L, where the set of generators naturally extends the sets of generators of G and L, and L admits a Cayley graph that is a tree. We show how one can compute the conjugacy growth series of such groups in terms of the standard and conjugacy growth series of G. We then provide explicit formulas for groups of the form G\wr ℤ and G\wr (C2*C2). We also prove that the radius of convergence of the conjugacy growth series of G\wr L, for any G and L as above, is the same as the radius of convergence of its standard growth series.