Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Francis Buekenhout, Julie De Saedeleer, and Dimitri Leemans

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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


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