Webs related to K-loops and reflection structures

Gabrieli, Elisabetta; Im, Bokhee; Karzel, Helmut

doi:10.1007/bf02940865

Cited by 12 publications

(2 citation statements)

References 15 publications

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“…This stimulated a steady flurry of activity aimed at generalizing this correspondence. On the one hand, loops have been related to chain structures (see [3,7]) whereas, on the other hand, some classes of loops (L, +) have been represented by suitable edge-colored complete graphs (see [8,9,16]). The latter realization is based on the fact that both structures can be obtained by a suitable selected set J of involutions acting transitively or regularly on the set L. Actually any regular involution set (L,J ), together with the choice of an element o ∈ L gives rise as well to a so-called involutorial difference loop (L, +) (briefly ID-loop, see Sect.…”

Section: Introductionmentioning

confidence: 99%

Loops with two-sided inverses constructed by a class of regular permutation sets

Pasotti

Zizioli

2011

J. Geom.

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In this paper we present a technique for building a new loop starting from the loops (K, +), (P, +) and (P, +) fulfilling suitable conditions, generalizing the construction presented in Zizioli (J Geom 95(1-2):173-186, 2009) where K = Z2 or K = Z3 and (P, +) is an abelian group. We investigate the dependence of the properties of the new loop on the corresponding properties of the initial ones (associativity, Bol condition, automorphic inverse property, Moufang condition), and we provide some examples.Mathematics Subject Classification (2010). Primary 20N05.

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Section: Introductionmentioning

confidence: 99%

Loops with two-sided inverses constructed by a class of regular permutation sets

Pasotti

Zizioli

2011

J. Geom.

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“…Kroll in [5] and used by further authors (B. Alinovi, E. Gabrieli, B. Im, J. Kosiorek, A. Matraś and C. Tonesi c.f. [1][2][3][4] and [7]). In these papers we find a begin of a theory of chain structures.…”

Section: Introduction and Notationsmentioning

confidence: 99%