Polynomials for primitive nonsolvable permutation groups of degree d ⩽ 15

Diameters of Degree Graphs of Nonsolvable Groups

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

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...

Four-Vertex Degree Graphs of Nonsolvable Groups

For a finite group G, the character degree graph ∆(G) is the graph whose vertices are the primes dividing the degrees of the ordinary irreducible characters of G, with distinct primes p and q joined by an edge if pq divides some character degree of G. We determine all graphs with four vertices that occur as ∆(G) for some nonsolvable group G. Along with previously known results on character degr...

Connectedness of Degree Graphs of Nonsolvable Groups