Analogues of the Jordan-Holder theorem for transitive G-sets

Details Analogues of the Jordan-Holder theorem for transitive G-sets Analogues of the Jordan-Holder theorem for transitive G-sets

2007-12-26

arxiv.org/abs/0712.4142v1

Mathematics

Group Theory

Scientific paper

Let G be a transitive group of permutations of a finite set X, and suppose that some element of G has at most two orbits on X. We prove that any two maximal chains of groups between G and a point-stabilizer of G have the same length, and the same sequence of relative indices between consecutive groups (up to permutation). We also deduce the same conclusion when G has a transitive quasi-Hamiltonian subgroup.

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