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- W2979173856 abstract "We show that the automorphism group of a one-dimensional full shift (the group of reversible cellular automata) does not satisfy the Tits alternative. That is, we construct a finitely-generated subgroup which is not virtually solvable yet does not contain a free group on two generators. We give constructions both in the two-sided case (spatially acting group $mathbb Z$) and the one-sided case (spatially actingmonoid $mathbb N$, alphabet size at least eight). Lack of Tits alternative follows for several groups of symbolic (dynamical) origin: automorphism groups of two-sided one-dimensional uncountable sofic shifts, automorphism groups of multidimensional subshifts of finite type with positive entropy and dense minimal points, automorphism groups of full shifts over non-periodic groups, and the mapping class groups of two-sided one-dimensional transitive SFTs. We also show that the classical Tits alternative applies to one-dimensional (multi-track) reversible linear cellular automata over a finite field." @default.
- W2979173856 created "2019-10-10" @default.
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- W2979173856 date "2019-09-30" @default.
- W2979173856 modified "2023-09-30" @default.
- W2979173856 title "No Tits alternative for cellular automata" @default.
- W2979173856 doi "https://doi.org/10.4171/ggd/529" @default.
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