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    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeJan 24th 2014
    • (edited Jan 25th 2014)

    So as to get rid of a grey unattached link, I created a stub for finitely presented group.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 24th 2014

    It’s certainly the definition that one will find in the literature, but I wonder if I’m alone in finding the grammar a little odd here. According to this definition, there is no difference in meaning between a “finitely presented group” and a “finitely presentable group”. But if it were up to me, I would refer to a finitely presented group only if I had a specific finite presentation in mind (a particular diagram exhibiting GG as a coequalizer of a pair of morphisms between finitely generated free groups).

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJan 24th 2014

    I agree with Todd. On the other hand, that’s what we get if we interpret “there is” in the propositions-as-types manner as a Σ\Sigma… (-:

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeJan 24th 2014

    In fact you both mirror the thought that came to me when I typed it out! I would also like to ask whether you feel that the isomorphism from the quotient group to GG should be part of the definition of a presentation. My preference is that it should be but that then it can be set aside.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeJan 24th 2014

    I have made a change to the entry. Try the new one for size!

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJan 27th 2014

    Re #4, of course it should be! I would tend to phrase it as “a presentation of GG is a coequalizer diagram FRFXGF R \rightrightarrows F X \twoheadrightarrow G”.

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeJan 27th 2014
    • (edited Jan 27th 2014)

    That sounds about right. As Ronnie and Johannes Huebschmann found in their paper on identities among relations, you need that to make sense of the identities.

    I have edited the entry accordingly.