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arXiv · 2105.10540

Separability and Randomness in Free Groups

Michal Buran
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Abstract

We prove new separability results about free groups. Namely, if $H_1, \ldots , H_k$ 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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Michal Buran. 2021-05-21. Separability and Randomness in Free Groups. https://arxiv.org/abs/2105.10540

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