Sharply 2-transitive linear groups
Group Theory
2013-02-21 v2 Algebraic Geometry
Rings and Algebras
Abstract
A group G is sharply 2-transitive if it admits a faithful permutation representation that is transitive and free on pairs of distinct points. Conjecturally, for all such groups there exists a near-field N (i.e. a skew field that is distributive only from the left) such that G is isomorphic to the semidirect product of the multiplicative and additive groups of N. This is well known in the finite case. We prove this conjecture when G < GL(n,F) is a linear group. Here we have to assume that both the characteristic of the field F and the permutational characteristic of the group G (see Definition 2.1) are not equal to 2.
Cite
@article{arxiv.1208.2427,
title = {Sharply 2-transitive linear groups},
author = {Yair Glasner and Dennis D. Gulko},
journal= {arXiv preprint arXiv:1208.2427},
year = {2013}
}
Comments
8 pages, revision matches accepted version