The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups
Group Theory
2014-12-15 v1
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.
Cite
@article{arxiv.1412.3912,
title = {The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups},
author = {Martin W. Liebeck and Cheryl E. Praeger and Jan Saxl},
journal= {arXiv preprint arXiv:1412.3912},
year = {2014}
}
Comments
18 pages