Abstract
We find a short equational basis for the variety of [Formula: see text]-supernilpotent loops. We also present a conceptually simple proof that [Formula: see text]-nilpotence and [Formula: see text]-supernilpotence are equivalent for groups. Connections between [Formula: see text]-supernilpotent loops, Moufang loops, code loops, automorphic loops and AIM loops are explored.
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