2024/05/26 by Alex C. Dantas, Dantas, Alex C., Junio R. Oliveira +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #FOS: Mathematics #Group Theory (math.GR) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2405.16678
openalex publication_date 2024/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular m-tree. We prove that if G is a subgroup of an automata group, then for each finitely generated abelian group A, the wreath product A \wr G is a subgroup of an automata group. We obtain, for example, that C2 \wr (C2 \wr ℤ), ℤ \wr (C2 \wr ℤ), C2 \wr (ℤ \wr ℤ), and ℤ \wr (ℤ \wr ℤ) are subgroups of automata groups. In the particular case ℤ \wr (ℤ \wr ℤ), we prove that it is a subgroup of a two-letters automata group; this solves Problem 15.19 - (b) of the Kourovka Notebook proposed by A. M. Brunner and S. Sidki in 2000 [8, 17].