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Jan 27, 2012 at 0:44 comment added Colin Reid Ah yes, of course.
Jan 26, 2012 at 18:38 comment added Benjamin Steinberg Colin, of course it is finite if the group is finite. There are only finitely many k-ary functions on the group. The fact that the finitely generated free object in the variety generated by a finite universal algebra goes back to Birkhoff.
Jan 26, 2012 at 16:32 history answered Colin Reid CC BY-SA 3.0