Algorithmically finite groups

Details Algorithmically finite groups Algorithmically finite groups

2010-12-08

arxiv.org/abs/1012.1653v1

Mathematics

Group Theory

Scientific paper

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.

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