EuDML | Browse

Using the geometry of the projective plane over the finite field $𝔽_{q}$ , we construct a Hermitian Lorentzian lattice $L_{q}$ of dimension $(q^{2} + q + 2)$ defined over a certain number ring $𝒪$ that depends on $q$ . We show that infinitely many of these lattices are $p$ -modular, that is, $p L_{q}^{'} = L_{q}$ , where $p$ is some prime in $𝒪$ such that ${| p |}^{2} = q$ .The Lorentzian lattices $L_{q}$ sometimes lead to construction of interesting positive definite lattices. In particular, if $q \equiv 3 mod 4$ is a rational prime such that $(q^{2} + q + 1)$ is norm of some element in $ℚ [\sqrt{- q}]$ , then we find a $2 q (q + 1)$ dimensional...

Currently displaying 41 – 60 of 125

Previous Page 3 Next

Displaying 41 – 60 of 125

Flocks in PG(3, q).

Frobenius collineations in finite projective planes.

Generalization flocks of $𝒬^{+} (3, q)$ .

Generalization of one Baer's theorem for nets

Geometric hyperquasigroups and line spaces

Homomorphisms of nets of fixed degree, with singular points on the same line

Hyperplane Coverings and Blocking Sets.

Il sottogruppo generato dalle involuzioni regolari di un $B$ -ovale $2$ -transitivo

Intersections in Projective Space I: Combinatorics.

Isomorphism of projective planes and isotopism of planar ternary rings

$k$ -arcs in finite Benz planes.

Kleine Desargues-Bedingung in Geweben

Kompakte, vier-dimensionale projektive Ebenen mit 8-dimensionaler Kollineationsgruppe.

Locally Truncated Buildings and M.... .

Mirror Property for Nonsingular Mixed Configurations of Lines and Points in R3 .

Modular lattices from finite projective planes

Multiquasigroups and weighted projective planes

Natural Bases for Subplanes of Free Completions.

Non-existence of Cartesian groups of order $2 p^{m}$

Non-Existence of Steiner Systems of Type S (d - 1, d, 2d).

Currently displaying 41 – 60 of 125