Notes on "A note on subgroups of automorphism groups of full shifts"

Alperin's paper:

I just (7th September 2017) found Alperin's paper when looking for something else: See here for a copy of the pdf on ResearchGate.

I was never able to find it, so I only cited the citation of it in Boyle-Lind-Rudolph. In hindsight, perhaps I could have guessed R. C. Alperin knows something about it. Though I never saw this note (that I can recall), my paper surely exists partially because I heard about this result several times, had to reconstruct a proof myself, and then took it a step further to make it worth my time.

Free products in automata groups and automatic groups

The "automorphism group of a full shift" is of course just a fancy name for the group of reversible cellular automata. There are other kinds of groups with "automaton" in their name: in particular automata groups and automatic groups. I do not know any connections between the three (except that groups of CA and automata groups are both subgroups of the rational group). Nevertheless, these classes have similar closure properties:

• In `Finite automaton actions of free products of groups' by Mariia Fedorova, Andriy Oliynyk, in Algebra and Discrete Mathematics, vol. 23, 2017, number 2, pp. 230–236 it is shown that the set of subgroups of automata groups (with all alphabets) is closed under free products. It is also closed under direct products.
• Also automatic groups are known to be closed under free and direct products.

Last update: 7.9.2017