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- Title
On abelian-by-cyclic Moufang loops.
- Authors
Drápal, Aleš; Vojtěchovský, Petr
- Abstract
We initiate a systematic study of abelian-by-cyclic Moufang loops, that is, Moufang loops Q with an abelian normal subgroup X such that Q / X is a cyclic group. Among other results, we construct all split abelian-by-cyclic Moufang loops in which both X and Q / X are 3-divisible, using so-called Moufang permutations on X, which are permutations that deviate from an automorphism of X by an alternating biadditive mapping. Additional abelian-by-cyclic Moufang loops are obtained from so-called construction pairs. As an aside, we show that, in a Moufang loop Q obtained from a construction pair, the abelian normal subgroup X induces an abelian congruence of Q if and only if Q is a group.
- Subjects
CYCLIC groups; PERMUTATIONS; PERMUTATION groups
- Publication
Forum Mathematicum, 2024, Vol 36, Issue 2, p339
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2022-0391