Sharply 2-transitive linear groups

Yair Glasner; Dennis D. Gulko

doi:10.1093/imrn/rnt014

Sharply 2-transitive linear groups

Yair Glasner, Dennis D. Gulko

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

A group Γ 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, see Definition 2) such that. This is well known in the finite case. We prove this conjecture when Γ<GL_n(F) is a linear group, where F is any field with char(F)≠2 and that p-char(Γ)≠2 (see Definition 2.2).

Original language	American English
Pages (from-to)	2691-2701
Number of pages	11
Journal	International Mathematics Research Notices
Volume	2014
Issue number	10
DOIs	https://doi.org/10.1093/imrn/rnt014
State	Published - 1 Jan 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnt014

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N2 - A group Γ 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, see Definition 2) such that. This is well known in the finite case. We prove this conjecture when Γn(F) is a linear group, where F is any field with char(F)≠2 and that p-char(Γ)≠2 (see Definition 2.2).

AB - A group Γ 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, see Definition 2) such that. This is well known in the finite case. We prove this conjecture when Γn(F) is a linear group, where F is any field with char(F)≠2 and that p-char(Γ)≠2 (see Definition 2.2).

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JF - International Mathematics Research Notices

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Sharply 2-transitive linear groups

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