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For what sort of groups are the Dehn's Fundamental Problems solvable,that is for what sort of groups are the word,conjugacy and isomorphism problems solvable.

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  • $\begingroup$ In my experience the word problem tends to be solvable in all (finitely generated) groups, except for those that have been specifically constructed to have unsolvable word problem. But this is far from being true of the conjugacy and isomorphism problems. $\endgroup$
    – Derek Holt
    Mar 12, 2014 at 13:41
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    $\begingroup$ I would recommend the survey article here for introductory reading: ms.unimelb.edu.au/~cfm/papers/paperpdfs/msri_survey.all.pdf $\endgroup$
    – Derek Holt
    Mar 12, 2014 at 13:49
  • $\begingroup$ Miller's survey article (which Derek Holt has linked to) is certainly the best reference for this, but the question as stated is far too broad. What sort of groups are you interested in? $\endgroup$
    – HJRW
    Mar 13, 2014 at 7:48

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