English

On a finite state representation of $GL(n,\mathbb{Z})$

Group Theory 2023-09-06 v1

Abstract

It is examined finite state automorphisms of regular rooted trees constructed to represent groups GL(n,Z)GL(n,\mathbb{Z}). The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of GL(2,Z)GL(2,\mathbb{Z}) over an alphabet of size 44 a finite state representation of the free group of rank 22 over binary alphabet is constructed.

Keywords

Cite

@article{arxiv.2309.01241,
  title  = {On a finite state representation of $GL(n,\mathbb{Z})$},
  author = {Andriy Oliynyk and Veronika Prokhorchuk},
  journal= {arXiv preprint arXiv:2309.01241},
  year   = {2023}
}