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Congruence solvability in finite Moufang loops of order coprime to three

2023/01/09 by Aleš Drápal, Drápal, Aleš, Petr Vojtěchovský +1
Mathematics · Engineering · #Mathematics and Applications #graph theory and CDMA systems #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2301.03680

Abstract

We prove that a normal subloop X of a Moufang loop Q induces an abelian congruence of Q if and only if each inner mapping of Q restricts to an automorphism of X and u(xy) = (uy)x for all x,y∈ X and u∈ Q. The former condition can be omitted when X is 3-divisible. This characterization is then used to show that classically solvable finite 3-divisible Moufang loops are congruence solvable.

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