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).

Pianta, S., Karzel, H., Zizioli, E., K-loops derived from Frobenius groups, <<DISCRETE MATHEMATICS>>, 2002; (255, no. 1-3): 225-234 [http://hdl.handle.net/10807/55455]

K-loops derived from Frobenius groups

Pianta, Silvia;Karzel, Helmut;Zizioli, Elena
2002

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).
eng
Pianta, S., Karzel, H., Zizioli, E., K-loops derived from Frobenius groups, <>, 2002; (255, no. 1-3): 225-234 [http://hdl.handle.net/10807/55455]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/55455
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact