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Department of Mathematics,
University of California San Diego

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Undergraduate Honors Presentation

Richard Li

University of California, San Diego

An Embedding of the Commutator Subgroup into the Automorphism Group of the Full Shift

Abstract:

Let $A$ be a finite alphabet. The automorphism group $\mathrm{Aut}(A^\mathbb{Z})$ is the group of invertible sliding block codes from the full $A$-shift to itself. Suppose $N\trianglelefteq\mathrm{Aut}(A^\mathbb{Z})$. By emulating methods from Kim and Roush's embedding, we show that either $N\le\mathbb{Z}$ or the commutator subgroup $[\mathrm{Aut}(2^\mathbb{Z}),\mathrm{Aut}(2^\mathbb{Z})]$ embeds into $N$. It is known that the free group on $2$ generators embeds into this commutator subgroup.

Host: Joshua Frisch

May 7, 2026

3:00 PM

APM 5829

Research Areas

Ergodic Theory and Dynamical Systems

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