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

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Bering, Edgar A, Studenmund, Daniel
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.11.2021
Subjects
Group theory
Isomorphism
Subgroups
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Summary: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.
ISSN:2331-8422