Galois Graphs: Walks, Trees and Automorphisms |
| |
Authors: | Josep M. Brunat Joan-C. Lario |
| |
Affiliation: | (1) Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo, 5, 08028- Barcelona, Catalunya, Spain |
| |
Abstract: | Given a symmetric polynomial (x, y) over a perfect field k of characteristic zero, the Galois graph G() is defined by taking the algebraic closure as the vertex set and adjacencies corresponding to the zeroes of (x, y). Some graph properties of G(), such as lengths of walks, distances and cycles are described in terms of . Symmetry is also considered, relating the Galois group Gal(/k) to the automorphism group of certain classes of Galois graphs. Finally, an application concerning modular curves classifying pairs of isogeny elliptic curves is revisited. |
| |
Keywords: | Galois graph digraph tree automorphism |
本文献已被 SpringerLink 等数据库收录! |
|