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arXiv · 2111.06577

Hall's universal group is a subgroup of the abstract commensurator of a free group

Edgar A. Bering IV·Daniel Studenmund
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Abstract

P. Hall constructed a universal countable locally finite group U, determined up to isomorphism by two properties: every finite group C is a subgroup of U, and every embedding of C into U is conjugate in U. Every countable locally finite group is a subgroup of U. We prove that U is a subgroup of the abstract commensurator of a finite-rank nonabelian free group.

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Edgar A. Bering IV, Daniel Studenmund. 2021-11-12. Hall's universal group is a subgroup of the abstract commensurator of a free group. https://arxiv.org/abs/2111.06577

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