A generalization of Ito's theorem to skew braces

The famous theorem of Ito' in group theory states that if a group G = HK is the product of two abelian subgroups H and K, then G is metabelian. We shall generalize this to the setting of a skew brace (A, center dot, degrees). Our main result says that if A = BC or A = B degrees C is the product of two trivial sub skew braces B and C which are both left and right ideals in the opposite skew brace of A, then A is meta-trivial. One can recover Ito''s theorem by taking A to be an almost trivial skew brace. (c) 2023 Elsevier Inc. All rights reserved.