Andriy Oliynyk

collaborators

3 papers

math.GR2023

On a finite state representation of $G L (n, Z)$

Andriy Oliynyk, Veronika Prokhorchuk

It is examined finite state automorphisms of regular rooted trees constructed to represent groups $G L (n, Z)$ . The number of states of automorphisms that correspond to eleme…

math.GR2023

On exponentiation, $p$ -automata and HNN extensions of free abelian groups

Andriy Oliynyk, Veronika Prokhorchuk

For every prime $p$ it is shown that a wide class of HNN extensions of free abelian groups admit faithful representation by finite $p$ -automata.

math.GR2023

On (bi)reversible automata generating lamplighter groups

Piotr W. Nowak, Andriy Oliynyk, Veronika Prokhorchuk

For any nontrivial abelian group $X$ we construct a reversible (bireversible in case the order of $X$ is odd) automaton such that its set of states and alphabet a…

On a finite state representation of GL(n,Z)

On exponentiation, p-automata and HNN extensions of free abelian groups

On (bi)reversible automata generating lamplighter groups

On a finite state representation of $G L (n, Z)$

On exponentiation, $p$ -automata and HNN extensions of free abelian groups