On \(K\)-loops of finite order

DOI10.1007/BF03323144zbMath0803.20052WikidataQ59383318 ScholiaQ59383318MaRDI QIDQ1320078

Alexander Kreuzer, Heinrich Wefelscheid

Publication date: 5 January 1995

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

permutationsaxiomsright loopsquasidirect productsconstruction methods for \(K\)-loopsfinite proper loops

Mathematics Subject Classification ID

Loops, quasigroups (20N05)

Related Items (18)

Gyrosemidirect product structure of bounded symmetric domains ⋮ Reflection groups and \(K\)-loops ⋮ Construction of a class of loops via graphs. ⋮ \(K\)-loops over dual numbers ⋮ A geometric construction of the K-loop of a hyperbolic space ⋮ Equivalence of two gyrogroup structures on unit balls ⋮ A construction of loops which admit right alternative loop rings ⋮ Geometry of kinematic \(K\)-loops ⋮ Reflection geometries over loops ⋮ Web loops and webs with reflections ⋮ \(K\)-loops from classical groups over ordered fields ⋮ Loops, reflection structures and graphs with parallelism. ⋮ A characterization of Bol left loops. ⋮ Webs related to \(K\)-loops and reflection structures ⋮ Groups with an involutory antiautomorphism and \(K\)-loops; application to space-time-world and hyperbolic geometry. I ⋮ Connections between loops of exponent 2, reflection structures and complete graphs with parallelism ⋮ Loops and semidirect products ⋮ Determination of the automorphism group of a hyperbolic \(K\)-loop

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