## 5 Citations

### On base sizes for primitive groups of product type

- MathematicsJournal of Pure and Applied Algebra
- 2022

### On the Saxl graphs of primitive groups with soluble stabilisers

- MathematicsAlgebraic Combinatorics
- 2022

Let G be a transitive permutation group on a ﬁnite set Ω and recall that a base for G is a subset of Ω with trivial pointwise stabiliser. The base size of G , denoted b ( G ), is the minimal size of…

### Strongly base-two groups

- Mathematics
- 2022

. Let G be a ﬁnite group, let H be a core-free subgroup and let b ( G, H ) denote the base size for the action of G on G/H . Let α ( G ) be the number of conjugacy classes of core-free subgroups H of…

### Fixed point ratios for finite primitive groups and applications

- MathematicsAdvances in Mathematics
- 2022

## References

SHOWING 1-10 OF 58 REFERENCES

### Base sizes for S-actions of finite classical groups

- Mathematics
- 2014

Let G be a permutation group on a set Ω. A subset B of Ω is a base for G if the pointwise stabilizer of B in G is trivial; the base size of G is the minimal cardinality of a base for G, denoted by…

### Base sizes for sporadic simple groups

- Mathematics
- 2010

Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise…

### On base sizes for symmetric groups

- Mathematics
- 2011

A base of a permutation group G on a set Ω is a subset B of Ω such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G…

### On Pyber's base size conjecture

- Mathematics
- 2013

Let G be a permutation group on a finite set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A…

### Base sizes for simple groups and a conjecture of Cameron

- Mathematics
- 2009

Let G be a permutation group on a finite set Ω. A base for G is a subset B ⊆ Ω with pointwise stabilizer in G that is trivial; we write b(G) for the smallest size of a base for G. In this paper we…

### 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…

### Bounds on finite quasiprimitive permutation groups

- MathematicsJournal of the Australian Mathematical Society
- 2001

Abstract A permutation group is said to be quasiprimitive if every nontrivial normal subgroup is transitive. Every primitive permutation group is quasiprimitive, but the converse is not true. In this…

### Trivial Set-Stabilizers in Finite Permutation Groups

- MathematicsCanadian Journal of Mathematics
- 1983

For which permutation groups does there exist a subset of the permuted set whose stabilizer in the group is trivial? The permuted set has so many subsets that one might expect that subsets with…