References
SHOWING 1-10 OF 37 REFERENCES
On the commuting probability of p-elements in a finite group
- Mathematics
- 2021
. Let G be a finite group, let p be a prime and let Pr p ( G ) be the probability that two random p -elements of G commute. In this paper we prove that Pr p ( G ) > ( p 2 + p − 1) /p 3 if and only if…
Base sizes for primitive groups with soluble stabilisers
- MathematicsAlgebra & Number Theory
- 2021
Let $G$ be a finite primitive permutation group on a set $\Omega$ with point stabiliser $H$. Recall that a subset of $\Omega$ is a base for $G$ if its pointwise stabiliser is trivial. We define the…
The spread of a finite group
- Mathematics
- 2020
A group $G$ is said to be $\frac{3}{2}$-generated if every nontrivial element belongs to a generating pair. It is easy to see that if $G$ has this property then every proper quotient of $G$ is…
Classical Groups, Derangements and Primes
- Mathematics
- 2016
Preface Notational conventions 1. Introduction 2. Finite classical groups 3. Conjugacy classes 4. Subspace actions 5. Non-subspace actions 6. Low-dimensional classical groups Appendix A.…
On the Order of Uniprimitive Permutation Groups
- Mathematics
- 1981
One of the central problems of 19th century group theory was the estimation of the order of a primitive permutation group G of degree n, where G X An. We prove I G I < exp (4V'/ n log2 n) for the…
On the Minimal Degree of a Primitive Permutation Group
- Mathematics
- 1998
Abstract We improve a result of Liebeck and Saxl concerning the minimal degree of a primitive permutation group and use it to strengthen a result of Guralnick and Neubauer on generic covers of…