A note on simple medial quasigroups
A solvable primitive group with finitely generated abelian stabilizers is finite.
A Problem of W.A. Manning on Primitive Permutation Groups.
B-groups of order a product of two distinct primes
Bounding the Rank of Certain Permutation Groups.
Des groupes transitifs de substitutions de degré et de classe
Estimation of Sylow Subgroups in Primitive Permutation Groups.
Extension of Some Results of Manning and Wielandt on Primitive Permutation Groups.
Extremely primitive groups and linear spaces
A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let be a nontrivial finite regular linear space and Suppose that is extremely primitive on points and let rank be the rank of on points. We prove that rank with few exceptions. Moreover, we show that is neither a sporadic group nor an alternating group, and with a Fermat prime if is a finite classical simple group.
Finiteness results for Hilbert's irreducibility theorem
Let be a number field, its ring of integers, and be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations such that is still irreducible. In this paper we study the set of those with reducible. We show that is a finite set under rather weak assumptions. In particular, previous results obtained by diophantine approximation techniques, appear as special cases of some of our results. Our method is different. We use elementary group...
Graphs and Finite Permutation Groups.
Graphs and Finite Permutation Groups. II.
On Permutation Groups of Degree 2p.
On the Degrees of Primitive Permutation Groups.
On the maximal subgroups of the finite classical groups.
On the Point Stabilizer in a Primitive Permutation Group.
Permutations which make transitive groups primitive
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups...
Polynomial Automorphisms Over Finite Fields
It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
Primitive Permutation Groups with Small Orbitals.
Sur la limite du degré des groupes primitifs qui contiennent une substitution donnée.
Sylow Subgroups of Transitive Permutation Groups.