most recent 30 from http://mathoverflow.net 2013-06-19T05:27:51Z http://mathoverflow.net/feeds/question/107357 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107357/group-presentations-with-few-relations-and-undecidable-word-problem bb 2012-09-17T05:08:25Z 2012-09-17T06:07:38Z

<p>This question came up in an algebra class I'm teaching. It's not my field and I couldn't find an answer easily, so I thought I would ask it here.</p> <p>Is the fewest number of relations in a presentation of a group with undecidable word problem known? </p> <p>The example with the fewest relations I could find by googling was 12 relations in a 1969 paper by Borisov (http://www.ams.org/mathscinet-getitem?mr=0260851) I also found a 1972 paper by Collins (http://www.ams.org/mathscinet-getitem?mr=0314998) which describes a presentation with 12 relations.</p>