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

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

2005-02-23

arxiv.org/abs/math/0502490v2

Mathematics

General Mathematics

6 pages, Latex2e

Scientific paper

By 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, groups

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