Geodesic
The Orbit-Stabilizer Problem for Linear Groups
Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 238-259

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a subgroup of the general linear group GL(n, Q) over the rational field Q, and consider its action by right multiplication on the vector space Q n of n-tuples over Q. The present paper investigates the question of how we may constructively determine the orbits and stabilizers of this action for suitable classes of groups. We suppose that G is specified by a finite set {x 1, ..., xr ) of generators, and investigate whether there exist algorithms to solve the two problems:(Orbit Problem) Given u, v ∊ Q n , does there exist x ∊ G such that ux = v; if so, find such an element x as a word in x 1, ..., xr and their inverses.(Stabilizer Problem) Given u, v ∊ Q n , describe all words in x 1, ..., xr and their inverses which lie in the stabilizer 
Dixon, John D. The Orbit-Stabilizer Problem for Linear Groups. Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 238-259. doi: 10.4153/CJM-1985-015-4
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