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Topological full groups of minimal subshifts and quantifying local embeddings into finite groups

Part of: Topological dynamics Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  05 April 2022

HENRY BRADFORD Open the ORCID record for HENRY BRADFORD [Opens in a new window]  and
DANIELE DONA Open the ORCID record for DANIELE DONA [Opens in a new window]
HENRY BRADFORD*
Affiliation:
Christ’s College, University of Cambridge, St Andrew’s Street, Cambridge, CB2 3BU, UK
DANIELE DONA
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus Givat Ram, The Hebrew University of Jerusalem, 9190401 Jerusalem, Israel (e-mail: [email protected])
*
e-mail: [email protected]
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Abstract

We investigate quantitative aspects of the locally embeddable into finite groups (LEF) property for subgroups of the topological full group of a two-sided minimal subshift over a finite alphabet, measured via the LEF growth function. We show that the LEF growth of may be bounded from above and below in terms of the recurrence function and the complexity function of the subshift, respectively. As an application, we construct groups of previously unseen LEF growth types, and exhibit a continuum of finitely generated LEF groups which may be distinguished from one another by their LEF growth.

Keywords

LEFtopological full groupminimal subshift

MSC classification

Primary: 20E26: Residual properties and generalizations; residually finite groups
Secondary: 20F69: Asymptotic properties of groups 37B10: Symbolic dynamics
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 5 , May 2023 , pp. 1492 - 1510
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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