Analogues of the Jordan–hölder Theorem for Transitive G-sets
نویسندگان
چکیده
Let G be a transitive group of permutations of a finite set Ω, and suppose that some element of G has at most two orbits on Ω. 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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