The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups

Martin W. Liebeck; Cheryl E. Praeger; Jan Saxl

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arXiv · 1412.3912

The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups

Martin W. Liebeck·Cheryl E. Praeger·Jan Saxl

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Abstract

A linear group G on a finite vector space V, (that is, a subgroup of GL(V)) is called (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 (1/2)-transitive linear groups. As a consequence we complete the determination of the finite (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 finite (k+1/2)-transitive permutation groups for integers k > 1.

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Martin W. Liebeck, Cheryl E. Praeger, Jan Saxl. 2014-12-12. The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups. https://arxiv.org/abs/1412.3912

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