A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä

No Tits alternative for cellular automata




TekijätVille Salo

KustantajaEuropean Mathematical Society Publishing House

KustannuspaikkaZürich

Julkaisuvuosi2019

JournalGroups, Geometry, and Dynamics

Lehden akronyymiGGD

Artikkelin numero13

Vuosikerta13

Numero4

Aloitussivu1437

Lopetussivu1455

Sivujen määrä19

ISSN1661-7207

eISSN1661-7215

DOIhttps://doi.org/10.4171/GGD/529

Verkko-osoitehttps://www.ems-ph.org/journals/show_pdf.php?issn=1661-7207&vol=13&iss=4&rank=13

Rinnakkaistallenteen osoitehttps://arxiv.org/abs/1709.00858


Tiivistelmä

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 Z) and the
one-sided case (spatially acting monoid 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.


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Last updated on 2024-26-11 at 23:12