JournalsjemsVol. 19, No. 10pp. 2895–2910

A sharply 2-transitive group without a non-trivial abelian normal subgroup

  • Eliyahu Rips

    Hebrew University, Jerusalem, Israel

  • Yoav Segev

    Ben-Gurion University, Beer-Sheva, Israel

  • Katrin Tent

    Universität Münster, Germany
A sharply 2-transitive group without a non-trivial abelian normal subgroup cover
Download PDF

Abstract

We show that any group is contained in some sharply 2-transitive group without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups that we construct have no fixed points.

Cite this article

Eliyahu Rips, Yoav Segev, Katrin Tent, A sharply 2-transitive group without a non-trivial abelian normal subgroup. J. Eur. Math. Soc. 19 (2017), no. 10, pp. 2895–2910

DOI 10.4171/JEMS/730