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Transitive Permutation Groups with Cyclic Point Stabilizers of Maximum Order |
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| Authors: | Andrea Lucchini Mario Mainardis Bernd Stellmacher |
| Affiliation: | (1) Dipartimento di Matematica, Università di Brescia, Via Valotti 9, I-25133 Brescia, Italy;(2) Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, I-33100 Udine, Italy;(3) Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Strasse 4, D-24098 Kiel, Germany |
| Abstract: | We prove that a transitive permutation group of degree n with a cyclic point stabilizer and whose order is n(n-1) is isomorphic to the affine group of degree 1 over a field with n elements. More generally we show that if a finite group G has an abelian and core-free Hall subgroup Q, then either Q has a small order (2|Q|2 < |G|) or G is a direct product of 2-transitive Frobenius groups. |
| Keywords: | transitive Frobenius groups Abelian Hall subgroups |
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