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. [doi:10.1016/S0012-365X(01)00400-9] [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).
2002
Inglese
Pianta, S., Karzel, H., Zizioli, E., K-loops derived from Frobenius groups, <<DISCRETE MATHEMATICS>>, 2002; (255, no. 1-3): 225-234. [doi:10.1016/S0012-365X(01)00400-9] [http://hdl.handle.net/10807/55455]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/55455
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