The primitive permutation groups of degree less than 2500

The primitive permutation groups of degree less than 2500

In this paper we use the O’Nan–Scott Theorem and Aschbacher’s theorem to classify the primitive permutation groups of degree less than 2500. MSC: 20B15, 20B10 1 Historical Background The classification of the primitive permutation groups of low degree is one of the oldest problems in group theory. The earliest significant progress was made by Jordan, who in 1871 counted the primitive permutatio...

The affine primitive permutation groups of degree less than 1000

In this paper we complete the classification of the primitive permutation groups of degree less than 1000 by determining the irreducible subgroups of GL(n, p) for p prime and pn < 1000. We also enumerate the maximal subgroups of GL(8, 2), GL(4, 5) and GL(6, 3). © 2003 Elsevier Science Ltd. All rights reserved. MSC: 20B10; 20B15; 20H30

Distinguishing Primitive Permutation Groups

Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.

Factorizations of Primitive Permutation Groups

On the Orders of Primitive Permutation Groups

The problem of bounding the order of a permutation group G in terms of its degree n was one of the central problems of 19th century group theory (see [4]). It is closely related to the 1860 Grand Prix problem of the Paris Academy, but its history goes in fact much further back (see e.g. [3], [1] and [10]). The heart of the problem is of course the case where G is a primitive group. The best res...