The analog of Grün's lemma holds for perfect two-sided skew braces using the annihilator but not for general perfect skew braces.
Nasybullov, Connections between properties of the additive and the multiplicative groups of a two- sided skew brace, J
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On Gr\"{u}n's lemma for perfect skew braces
The analog of Grün's lemma holds for perfect two-sided skew braces using the annihilator but not for general perfect skew braces.