2006/07/22 by Benjamin Steinberg, Steinberg, Benjamin
Mathematics · #20E08 #20E22 #20F38 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.CO #math.GR #msc:20E08 #msc:20E22 #msc:20F38
paper · pdf · doi:10.48550/arxiv.math/0607563
arxiv created 2006/07/22 · openalex publication_date 2006/07/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a partial solution a question of Grigorchuk, Nekrashevych, Sushchanskii and Šunik by giving an algorithm to test whether a finite state element of an infinite iterated (permutational) wreath product G = \mathbb Z/k\mathbb Z\wr \mathbb Z/k\mathbb Z\wr \mathbb Z/k\mathbb Z\wr >... of cyclic groups of order n acts spherically transitively. We can also decide whether two finite state spherically transitive elements of G are conjugate. For general infinite iterated wreath products, an algorithm is presented to determine whether two finite state automorphisms have the same image in the abelianization.