Separability and Randomness in Free Groups

2021/05/21 by Buran, Michal
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2105.10540

Abstract

We prove new separability results about free groups. Namely, if H₁, … , H_k are infinite index, finitely generated subgroups of a non-abelian free group F, then there exists a homomorphism onto some alternating group f:F \twoheadrightarrow A_m such that whenever H_i is not conjugate into H_j, then f(H_i) is not conjugate into f(H_j). The proof is probabilistic. We count the expected number of fixed points of f(H_i)'s and their subgroups under a carefully constructed measure.

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