The $k$-orbit theory and Fein-Kantor-Schacher Theorem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95179By the investigation of $k$-orbits symmetry properties it is obtained a simple proof of the B. Fein, W. M. Kantor and M. Schacher Theorem: any transitive permutation group contains a non-trivial fixed-point-free prime-power element. Key words: $k$-orbits, partitions, permutations, symmetry, groups6 pages, Latex2eGeneral Mathematics20C99The $k$-orbit theory and Fein-Kantor-Schacher Theoremtext