What question did this study set out to answer?

The study aims to explore the LEF property of subgroups in topological full groups associated with minimal subshifts.

March 1, 2026Open Access

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

Key Points

The study aims to explore the LEF property of subgroups in topological full groups associated with minimal subshifts.
Investigated LEF growth function in relation to recurrence and complexity functions.
Constructed examples of groups with unique LEF growth properties.
Exhibited a diverse set of finitely generated LEF groups.
Demonstrated that LEF growth can be bounded by recurrence and complexity functions.
Created groups with novel LEF growth types, broadening the understanding of LEF properties.
Established a continuum of finitely generated LEF groups, differing based on LEF growth.

Abstract

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.

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Cite This Study

BRADFORD et al. (Mon,) studied this question.

synapsesocial.com/papers/69a3d856ec16d51705d2f1ed https://doi.org/https://doi.org/10.17863/cam.125514

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