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- W2746248052 abstract "Suppose $(X,sigma)$ is a subshift, $P_X(n)$ is the word complexity function of $X$, and ${rm Aut}(X)$ is the group of automorphisms of $X$. We show that if $P_X(n)=o(n^2/log^2 n)$, then ${rm Aut}(X)$ is amenable (as a countable, discrete group). We further show that if $P_X(n)=o(n^2)$, then ${rm Aut}(X)$ can never contain a nonabelian free semigroup (and, in particular, can never contain a nonabelian free subgroup). This is in contrast to recent examples, due to Salo and Schraudner, of subshifts with quadratic complexity that do contain such a semigroup." @default.
- W2746248052 created "2017-08-31" @default.
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- W2746248052 date "2018-12-11" @default.
- W2746248052 modified "2023-09-27" @default.
- W2746248052 title "The automorphism group of a shift of slow growth is amenable" @default.
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- W2746248052 doi "https://doi.org/10.1017/etds.2018.126" @default.
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