2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76425The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are obtained for other types. For type A a probabilistic interpretation is given in terms of card shuffling.Final galley versionGroup TheoryCombinatorics20G40;17B45text