English

Algorithmically finite groups

Group Theory 2010-12-09 v1

Abstract

We call a group GG {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of GG. We construct examples of recursively presented infinite algorithmically finite groups and study their properties. For instance, we show that the Equality Problem is decidable in our groups only on strongly (exponentially) negligible sets of inputs.

Keywords

Cite

@article{arxiv.1012.1653,
  title  = {Algorithmically finite groups},
  author = {A. Myasnikov and D. Osin},
  journal= {arXiv preprint arXiv:1012.1653},
  year   = {2010}
}
R2 v1 2026-06-21T16:55:10.421Z