English

Automata over a binary alphabet generating free groups of even rank

Group Theory 2007-05-23 v1

Abstract

We construct automata over a binary alphabet with 2n2n states, n2n\geq 2, whose states freely generate a free group of rank 2n2n. Combined with previous work, this shows that a free group of every finite rank can be generated by finite automata over a binary alphabet. We also construct free products of cyclic groups of order two via such automata.

Keywords

Cite

@article{arxiv.math/0610033,
  title  = {Automata over a binary alphabet generating free groups of even rank},
  author = {Benjamin Steinberg and Mariya Vorobets and Yaroslav Vorobets},
  journal= {arXiv preprint arXiv:math/0610033},
  year   = {2007}
}
R2 v1 2026-07-22T17:43:22.839Z