K-loops derived from Frobenius groups

Silvia Pianta, Helmut Karzel, Elena Zizioli, H. Karzel

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We consider a generalization of the representation of the so-called co-Minkowski plane (due to H. and R. Struve) to an abelian group (V, +) and a commutative subgroup G of Aut(V, +). If P = G x V satisfies suitable conditions then an invariant reflection structure (in the sense of Karzel (Discrete Math. 208/209 (1999) 387-409)) can be introduced in P which carries the algebraic structure of K-loop on P (cf. Theorem 1). We investigate the properties of the K-loop (P, +) and its connection with the semi-direct product of V and G. If G is a fixed point free automorphism group then it is possible to introduce in (P, +) an incidence bundle in such a way that the K-loop (P, +) becomes an incidence fibered loop (in the sense of Zizioli (J. Geom. 30 (1987) 144-151)) (cf. Theorem 3).
Original languageEnglish
Pages (from-to)225-234
Number of pages10
JournalDiscrete Mathematics
Publication statusPublished - 2002

Keywords

  • Frobenius group
  • Linear space
  • k-loop

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