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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Non-split linear sharply 2-transitive groups
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by Yair Glasner and Dennis D. Gulko PDF
Proc. Amer. Math. Soc. 149 (2021), 2305-2317 Request permission

Abstract:

We give examples of countable linear groups $\Gamma < \operatorname {SL}_{{\mathbf {3}}}({\mathbf {R}})$, 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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Additional Information
  • Yair Glasner
  • Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel
  • MR Author ID: 673281
  • ORCID: 0000-0002-6231-3817
  • Email: yairgl@math.bgu.ac.il
  • Dennis D. Gulko
  • Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel
  • MR Author ID: 1065319
  • Email: gulkod@math.bgu.ac.il
  • Received by editor(s): October 30, 2019
  • Received by editor(s) in revised form: July 26, 2020
  • Published electronically: March 16, 2021
  • Additional Notes: The research of both authors was partially funded by Israel Science Foundation grant ISF 2919/19.
  • Communicated by: Martin Liebeck
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2305-2317
  • MSC (2020): Primary 20B22
  • DOI: https://doi.org/10.1090/proc/15360
  • MathSciNet review: 4246784