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I know that all finite groups have presentations. I also know that some infinite groups have finite presentations. Is it possible to decide in finite time whether a presentation is a presentation of a finite group?

mathlander
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    As Qiaocho has said, the answer is no. The problem is however semi-decidable in the sense that if the group is finite then it is possible to prove that it is finite. – Derek Holt Oct 07 '22 at 18:14

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No, this and many other questions about finite presentations are undecidable by the Adyan-Rabin theorem.

Qiaochu Yuan
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