Webs related to \(K\)-loops and reflection structures

DOI10.1007/BF02940865zbMath0951.20052MaRDI QIDQ1969673

Elisabetta Gabrieli, Bokhee Im, Helmut Karzel

Publication date: 19 March 2000

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

zbMATH Keywords

websBruck loopsreflection structuresweak \(K\)-loops

Mathematics Subject Classification ID

Loops, quasigroups (20N05) Differential geometry of webs (53A60) Algebraization in linear incidence geometry (51A25)

Related Items (6)

Loops, reflection structures and graphs with parallelism. ⋮ Loops with two-sided inverses constructed by a class of regular permutation sets. ⋮ Symmetric 2-structures, a classification ⋮ Connections between loops of exponent 2, reflection structures and complete graphs with parallelism ⋮ In memoriam: Helmut Karzel (1928--2021) ⋮ Webs with rotation and reflection properties and their relations with certain loops

Cites Work

• Weakly associative groups
• Symmetrische Permutationsmengen
• On collineation groups generated by Bol reflections
• On \(K\)-loops of finite order
• Determination of the automorphism group of a hyperbolic \(K\)-loop
• Reflection groups and \(K\)-loops
• Reflection geometries over loops
• Point-reflection geometries, geometric K-loops and unitary geometries
• A geometric construction of the K-loop of a hyperbolic space
• Group-like structure underlying the unit ball in real inner product spaces
• Loops as Invariant Sections in Groups, and their Geometry
• Inner mappings of Bruck loops

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