Self-similar groups, automatic sequences, and unitriangular representations Academic Article uri icon


  • 2015, The Author(s). We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two separate notions of automaticity: groups generated by automata and automatic sequences. We also show that if the group acts on the tree by p-adic automorphisms, then the corresponding linear representation is a representation by infinite triangular matrices. We relate this observation with the notion of height of an automorphism of a rooted tree due to L. Kaloujnine.

published proceedings


author list (cited authors)

  • Grigorchuk, R., Leonov, Y., Nekrashevych, V., & Sushchansky, V.

citation count

  • 4

complete list of authors

  • Grigorchuk, R||Leonov, Y||Nekrashevych, V||Sushchansky, V

publication date

  • July 2016