Non-split linear Sharply 2-transitive groups

Yair Glasner; Dennis D. Gulko

doi:10.1090/proc/15360

Non-split linear Sharply 2-transitive groups

Yair Glasner, Dennis D. Gulko

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

We give examples of countable linear groups Γ < SL₃(R), with no nontrivial normal abelian subgroups, that admit a faithful sharply 2-transitive action on a set. Without the linearity assumption, such groups were recently constructed by Rips, Segev, and Tent in [J. Eur. Math. Soc. 19 (2017), pp. 2895–2910]. Our examples are of permutational characteristic 2, in the sense that involutions do not fix a point in the 2-transitive action.

Original language	American English
Pages (from-to)	2305-2317
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	6
DOIs	https://doi.org/10.1090/proc/15360
State	Published - 1 Jun 2021

Keywords

Linear groups
Sharply 2-transitive

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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10.1090/proc/15360

Cite this

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abstract = "We give examples of countable linear groups Γ < SL3(R), with no nontrivial normal abelian subgroups, that admit a faithful sharply 2-transitive action on a set. Without the linearity assumption, such groups were recently constructed by Rips, Segev, and Tent in [J. Eur. Math. Soc. 19 (2017), pp. 2895–2910]. Our examples are of permutational characteristic 2, in the sense that involutions do not fix a point in the 2-transitive action.",

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Non-split linear Sharply 2-transitive groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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