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- W4315705839 abstract "We study abelian-by-cyclic Moufang loops. We construct all split $3$-divisible abelian-by-cyclic Moufang loops from so-called Moufang permutations on abelian groups $(X,+)$, which are permutations that deviate from an automorphism of $(X,+)$ by an alternating biadditive mapping (satisfying certain properties). More generally, we obtain additional abelian-by-cyclic Moufang loops from so-called construction pairs. As an aside, we show that in the Moufang loops $Q$ obtained from a construction pair on $(X,+)$ the abelian normal subgroup $(X,+)$ induces an abelian congruence of $Q$ if and only if $Q$ is a group." @default.
- W4315705839 created "2023-01-12" @default.
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- W4315705839 date "2023-01-09" @default.
- W4315705839 modified "2023-09-30" @default.
- W4315705839 title "On abelian-by-cyclic Moufang loops" @default.
- W4315705839 doi "https://doi.org/10.48550/arxiv.2301.03683" @default.
- W4315705839 hasPublicationYear "2023" @default.
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