Residually finite algorithmically finite groups, their subgroups and direct products

Abstract

We construct an infinite finitely generated recursively presented residually finite algorithmically finite group $G$ answering thereby a question of Myasnikov and Osin. Moreover, $G$ is "very infinite" and "very algorithmically finite" in the sense that $G$ contains an infinite abelian normal subgroup while all finite Cartesian powers of $G$ are algorithmically finite (i.e., for any positive integer $n$, there is no algorithm which writes out an infinite sequence of pairwise different elements of $G^n$). We also state several related problems.

4 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: a reference added; minor correction

References in corpus (1)

• Golod-Shafarevich groups: a survey

Cited by in corpus (1)

• Computational complexity and the conjugacy problem