Lack of profinite rigidity among extensions with free quotient

2023/11/29 by Paweł Piwek, Piwek, Paweł\
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2311.18079

Abstract

We present a construction that yields infinite families of non-isomorphic semidirect products N \rtimes F_m sharing a specified profinite completion. Within each family, m ≥ 2 is constant and N is a fixed group. For m=2 we can take N to be free of rank ≥ 10, free abelian of rank ≥ 12, or a surface group of genus ≥ 5.

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