A note on subgroups of automorphism groups of full shifts

: Ville Salo

Publisher: Cambridge University Press

: 2018

: Ergodic Theory and Dynamical Systems

: 38

: 1588

: 1600

: 13

: 0143-3857

: 1469-4417

DOI: https://doi.org/10.1017/etds.2016.95

: https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/div-classtitlea-note-on-subgroups-of-automorphism-groups-of-full-shiftsdiv/E4E9E78448211F173CB9F6E8AFFEE750

: https://research.utu.fi/converis/portal/detail/Publication/18192344

We discuss the set of subgroups of the automorphism group of a full shift and submonoids of its endomorphism monoid. We prove closure under direct products in the monoid case and free products in the group case. We also show that the automorphism group of a full shift embeds in that of an uncountable sofic shift. Some undecidability results are obtained as corollaries.

SubshiftsOfFullShiftAutosJournalFixed.pdf