Left nilpotent skew braces of class 2 over nilpotent additive groups are right nilpotent of class at most 2+mr, and hence centrally nilpotent.
Ballester-Bolinches, R
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On left nilpotent skew braces of class 2
Left nilpotent skew braces of class 2 over nilpotent additive groups are right nilpotent of class at most 2+mr, and hence centrally nilpotent.