Stabilizers in Higman-Thompson groups

2021/04/12 by Belk, James, Hyde, James, Matucci, Francesco
#20E06 #20F05 #20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2104.05572

Abstract

We investigate stabilizers of finite sets of rational points in Cantor space for the Higman-Thompson groups V_n,r. We prove that the pointwise stabilizer is an iterated ascending HNN extension of V_n,q for any q≥ 1. We also prove that the commutator subgroup of the pointwise stabilizer is simple, and we compute the abelianization. Finally, for each n we classify such pointwise stabilizers up to isomorphism.

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