Sharply 2-transitive linear groups

Yair Glasner; Dennis D. Gulko

doi:10.1093/imrn/rnt014

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arXiv · 1208.2427

Sharply 2-transitive linear groups

Yair Glasner·Dennis D. Gulko

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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.

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BibTeX RIS

Yair Glasner, Dennis D. Gulko. 2013-02-20. Sharply 2-transitive linear groups. https://doi.org/10.1093/imrn%2Frnt014

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