Analogues of the Jordan-Holder theorem for transitive G-sets
Group Theory
2007-12-27 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0712.4142,
title = {Analogues of the Jordan-Holder theorem for transitive G-sets},
author = {Greg Kuperberg and Michael Zieve},
journal= {arXiv preprint arXiv:0712.4142},
year = {2007}
}