We classify the finite primitive permutation groups which have a cyclic subgroup with two orbits. This extends classical topics in permutation group theory, and has arithmetic consequences. By a theorem of C. L. Siegel, affine algebraic curves with infinitely many integral points are parametrized by rational functions whose monodromy groups have this property. We classify the possibilities for these monodromy groups, and we give applications to Hilbert’s irreducibility theorem.
@article{ASNSP_2013_5_12_2_369_0, author = {M\"uller, Peter}, title = {Permutation groups with a cyclic two-orbits subgroup and monodromy groups of {Laurent} polynomials}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {369--438}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 12}, number = {2}, year = {2013}, mrnumber = {3114008}, zbl = {1366.20001}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2013_5_12_2_369_0/} }
TY - JOUR AU - Müller, Peter TI - Permutation groups with a cyclic two-orbits subgroup and monodromy groups of Laurent polynomials JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2013 SP - 369 EP - 438 VL - 12 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2013_5_12_2_369_0/ LA - en ID - ASNSP_2013_5_12_2_369_0 ER -
%0 Journal Article %A Müller, Peter %T Permutation groups with a cyclic two-orbits subgroup and monodromy groups of Laurent polynomials %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2013 %P 369-438 %V 12 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2013_5_12_2_369_0/ %G en %F ASNSP_2013_5_12_2_369_0
Müller, Peter. Permutation groups with a cyclic two-orbits subgroup and monodromy groups of Laurent polynomials. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 2, pp. 369-438. http://archive.numdam.org/item/ASNSP_2013_5_12_2_369_0/
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