English

Bounded Generation of Submonoids of Heisenberg Groups

Group Theory 2024-05-10 v1 Discrete Mathematics Formal Languages and Automata Theory

Abstract

If GG is a nilpotent group and [G,G][G,G] has Hirsch length 11, then every f.g. submonoid of GG is boundedly generated, i.e. a product of cyclic submonoids. Using a reduction of Bodart, this implies the decidability of the submonoid membership problem for nilpotent groups GG where [G,G][G,G] has Hirsch length 22.

Keywords

Cite

@article{arxiv.2405.05939,
  title  = {Bounded Generation of Submonoids of Heisenberg Groups},
  author = {Doron Shafrir},
  journal= {arXiv preprint arXiv:2405.05939},
  year   = {2024}
}