Dear Colleagues, The question Michael asked has already been answered by several people. However I would like to comment on Tim's "EXPLICITLY": A simplicial group is a simplicial object in the category of groups, which is a Mal'tsev category (some people use wrong spelling "Mal'cev"), and - as I know from Aurelio Carboni - every simplicial object in a Mal'tsev category is a Kan complex. This also tells me that the formulae Tim is mentioning should in fact involve just the Mal'tsev operation m (recall that for groups one can put m(x,y,z) = x-y+z for the m, in the additive notation). There must be something like this in Jonathan Smith's "Mal'tsev varieties". George Janelidze Prof T Porter wrote:
Dear Mike and everyone,
There is a proof in Peter May's little book and some indication in the survey article by Curtis (but his formaule do not work). The nice thing about the result is not that it is true but that it is possible to construct formulae for the fillers EXPLICITLY from the information on the horns. Heiner Kamps and myself used this approach in our book and it seemed to us better to introduce the problem and then get the reader to investigate the algorithmic idea rather than giving the solution as the latter does not tell you where the formulae came from.
Robert Knighten's reference to being in Moore's seminar notes is the earliest I have seen it as well.
Tim Porter