Abstract
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.
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