The classification of \frac{3}2-transitive permutation groups and \frac{1}2-transitive linear groups

Liebeck, Martin; Praeger, Cheryl; Saxl, Jan

doi:10.1090/proc/13243

The classification of $\frac {3}{2}$-transitive permutation groups and $\frac {1}{2}$-transitive linear groups
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by Martin W. Liebeck, Cheryl E. Praeger and Jan Saxl PDF

Proc. Amer. Math. Soc. 147 (2019), 5023-5037 Request permission

Abstract:

A linear group $G\le GL(V)$, where $V$ is a finite vector space, is called $\frac {1}{2}$-transitive if all the $G$-orbits on the set of nonzero vectors have the same size. We complete the classification of all the $\frac {1}{2}$-transitive linear groups. As a consequence we complete the determination of the finite $\frac {3}{2}$-transitive permutation groups – the transitive groups for which a point-stabilizer has all its nontrivial orbits of the same size. We also determine the $(k+\frac {1}{2})$-transitive groups for integers $k\ge 2$.

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