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...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 261; no. 1; pp. 493 - 500
Main Authors Bering, Edgar A., Studenmund, Daniel
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.06.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Group theory
Group Theory and Generalizations
Isomorphism
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Subgroups
Theoretical
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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:0021-2172
1565-8511
DOI:10.1007/s11856-023-2591-8