39 citations · 72 across the 10 of their papers we have counts for
10 papers
Regular orbits of symmetric and alternating groups
Joanna B. Fawcett, E. A. O'Brien, Jan Saxl
Given a finite group and a faithful irreducible -module where has prime order, does have a regular orbit on ? This problem is equivalent to determining which…
The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups
Martin W. Liebeck, Cheryl E. Praeger, Jan Saxl
A linear group G on a finite vector space V, (that is, a subgroup of GL(V)) is called (1/2)-transitive if all the G-orbits on the set of nonzero vectors have the same size. We comp…
On base sizes for algebraic groups
Timothy Burness, Robert Guralnick, Jan Saxl
Let be a permutation group on a set . A subset of is a base for if its pointwise stabilizer is trivial; the base size of is the minimal cardinality of a base. In…
Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type
Gerhard Heide, Jan Saxl, Pham Huu Tiep +1
Let be a finite simple group of Lie type, and let be the permutation representation of associated with the action of on itself by conjugation. We prove that every…
Arithmetic results on orbits of linear groups
Michael Giudici, Martin W. Liebeck, Cheryl E. Praeger +2
Let be a prime and a subgroup of . We define to be -exceptional if it has order divisible by , but all its orbits on vectors have size coprime to . We…
The classification of almost simple -transitive groups
John Bamberg, Michael Giudici, Martin W. Liebeck +2
A finite transitive permutation group is said to be 3/2-transitive if all the nontrivial orbits of a point stabilizer have the same size greater than 1. Examples include the 2-tran…