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

2014/06/02 by Rips, Eliyahu, Segev, Yoav, Tent, Katrin · 1 citation
#20B22 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1406.0382

Abstract

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

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• Sharply 2-transitive groups
• Sharply 2-transitive groups in characteristic 0
• Simple sharply 2-transitive groups
• Sharply 3-transitive groups
• Non-split linear sharply 2-transitive groups