A. Myasnikov, D. Osin
Published 2010-12-08Version 1
We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. 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.
Knuth-Bendix for groups with infinitely many rules
Partial Word and Equality problems and Banach densities
Constructing groups of type $FP_2$ over fields but not over the integers
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