Supernilpotent groups and $3$-supernilpotent loops

Published 16 Sep 2022 in math.GR | (2209.08128v2)

Abstract: We find a short equational basis for the variety of $3$-supernilpotent loops. We also present a conceptually simple proof that $k$-nilpotence and $k$-supernilpotence are equivalent for groups. Connections between $3$-supernilpotent loops, Moufang loops, code loops, automorphic loops and AIM loops are explored.

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