Non-split linear sharply 2-transitive groups

2016/08/14 by Glasner, Yair, Gulko, Dennis D.
#FOS: Mathematics #Group Theory (math.GR) #Primary 20B22

paper · doi:10.48550/arxiv.1608.04085

Abstract

We give examples of countable linear groups in SL_n(R) for n ≥ 3, 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. Our examples are of permutational characteristic 2, in the sense that involutions do not fix a point in the 2-transitive action.

Related

• A sharply 2-transitive group without a non-trivial abelian normal subgroup
• Sharply 2-transitive groups
• Non-split sharply 2-transitive groups of bounded exponent
• Non-split sharply 2-transitive groups of odd positive characteristic
• Sharply 2-transitive groups in characteristic 0