## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 23, Number 1 (2016), 33-55.

### Two-transitive pairs in $ \mathrm{PSL}(2,q)$

Francis Buekenhout, Julie De Saedeleer, and Dimitri Leemans

#### Abstract

For every group $ \mathrm{PSL}(2,q)$, $q$ a prime power, we classify all two-transitive pairs $(U,U_0)$ consisting of a subgroup $U$ of $ \mathrm{PSL}(2,q)$ and a subgroup $U_0$ of $U$ such that the action of $U$ on the cosets of $U_0$ is two-transitive. We obtain twenty classes up to conjugacy in $ \mathrm{PSL}(2,q)$ or fusion in $P\Gamma L (2,q)$ except for two cases in which we don't have that control.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 1 (2016), 33-55.

**Dates**

First available in Project Euclid: 9 March 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1457560852

**Digital Object Identifier**

doi:10.36045/bbms/1457560852

**Mathematical Reviews number (MathSciNet)**

MR3471977

**Zentralblatt MATH identifier**

1356.20002

**Subjects**

Primary: 20B20: Multiply transitive finite groups 20G40: Linear algebraic groups over finite fields

**Keywords**

projective special linear groups two-transitive action

#### Citation

Buekenhout, Francis; De Saedeleer, Julie; Leemans, Dimitri. Two-transitive pairs in $ \mathrm{PSL}(2,q)$. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 1, 33--55. doi:10.36045/bbms/1457560852. https://projecteuclid.org/euclid.bbms/1457560852