Groupes d'isométries permutant doublement transitivement un ensemble de droites vectorielles
| dc.creator | Vienne, Lucas | |
| dc.date | 2009-03-05 | |
| dc.date.accessioned | 2026-07-07T12:49:15Z | |
| dc.date.available | 2026-07-07T12:49:15Z | |
| dc.description | Let X be a non-empty finite set, E be a finite dimensional euclidean vector space and G a finite subgroup of O(E), the orthognal group of E. Suppose GG={U_i | i in X} is a finite set of linear lines in E and an orbit of G on which its operation is twice transitive. Then GG is an equiangular set of lines, which means that we can find a real number "c", and generators u_i of the lines U_i (i in X) such that forall i,j in X, ||u_i||=1, and if i is different from j then (u_i|u_j)=\gve_{i,j}.c, with \gve_{i,j} in {-1,+1\} Let Gamma be the simple graph whose set of vertices is X, two of them, say i and j, being linked when \gve_{i,j} = -1. In this article we first explore the relationship between double transitivity of G and geometric properties of Gamma. Then we construct several graphs associated with a twice transitive group G, in particular any of Paley's graphs is associated with a representation of G=PSL_2(q) on a set of q+1 equiangular lines in a vector space whose dimension is (q+1)/2. | |
| dc.identifier | https://arxiv.org/abs/0903.0912 | |
| dc.identifier | http://arxiv.org/abs/0903.0912 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222335 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05C25; 05C50; 05C62; 20B20; 20B05; 20B25 | |
| dc.title | Groupes d'isométries permutant doublement transitivement un ensemble de droites vectorielles | |
| dc.type | text |