33,623 research outputs found
Axioms for trimedial quasigroups
We give new equations that axiomatize the variety of trimedial quasigroups.
We also improve a standard characterization by showing that right semimedial,
left F-quasigroups are trimedial.Comment: 6 pages, AMS-LaTeX. To appear in Comment. Math. Univ. Carolinae. for
a special issue: the Proceedings of Loops03. Version 3: the proof of the main
result is collected together more formally; other stylistic change
A Generalization of Moufang and Steiner Loops
We study a variety of loops, RIF, which arise naturally from considering
inner mapping groups, and a somewhat larger variety, ARIF. All Steiner and
Moufang loops are RIF, and all flexible C-loops are ARIF. We show that all ARIF
loops are diassociative, thus generalizing Moufang's Theorem.Comment: 19 pp., 1 fig., uses amsart.cls, pifont.sty; to appear in Algebra
Universali
Finite Bruck loops
Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops X, showing that X is essentially the direct product of a Bruck loop of odd order with a 2-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 2-element Bruck loops are 2-loops, leaving open the question of whether such obstructions actually exist
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