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

abstract

• 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.

authors

• Grigorchuk, Rostislav
• Nekrashevych, Volodymyr

published proceedings

• BULLETIN OF MATHEMATICAL SCIENCES

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

publisher

• World Scientific Publishing  Publisher

published in

• Bulletin of Mathematical Sciences  Journal

keywords

• Automata Groups
• Automatic Matrices
• Automatic Sequences
• Groups Acting On Rooted Trees
• Self-similar Groups
• Wreath Products

Digital Object Identifier (DOI)

• 10.1007/s13373-015-0077-7

URI

• https://hdl.handle.net/1969.1/181761

start page

• 231

end page

• 285

volume

• 6

issue

• 2

URL

• http://dx.doi.org/10.1007/s13373-015-0077-7