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

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

The Structure of F-Quasigroups

We solve a problem of Belousov which has been open since 1967: to characterize the loop isotopes of F-quasigroups. We show that every F-quasigroup has a Moufang loop isotope which is a central product of its nucleus and Moufang center. We then use the loop to reveal the structure of the associated F-quasigroup.Comment: 24 pages. v.2 incorporates minor changes suggested by the referee. To appear in the Journal of Algebr

Ken Kunen: Algebraist

This paper is a greatly expanded version of a talk I gave in April 2009 at KunenFest. It describes Ken's work in algebra, particularly using automated deduction tools.Comment: 7 pages, to appear in a special issue of Topology and its Applications in honor of Ken Kune