Residually finite algorithmically finite groups, their subgroups and direct products
A. A. Klyachko, A. K. Mongush · Mathematical Notes · 2015
We construct a finitely generated infinite recursively presented residually finite algorithmically finite group G, thus answering a question of Myasnikov and Osin. The group G here is “strongly infinite” and “strongly algorithmically finite,” which means that G contains an infinite Abelian normal subgroup and all finite Cartesian powers of G are algorithmically finite (i.e., for any n, there is no algorithm writing out infinitely many pairwise distinct elements of the group G n ). We also formulate several open questions concerning this topic.