Non-split linear sharply 2-transitive groups, after Rips-Segev-Tent Academic Article uri icon

abstract

  • Abstract. We construct examples of countable linear groups Γ < SLn(R) with no non-trivial normal abelian subgroup that admit a faithful, sharply 2-transitive action on a set. The stabilizer of a point in the this action does not contain an involution … A sharply 2-transitive group is, by definition, a permutation group Γ … Question 1.1. Is every sharply 2-transitive group split … In Theorem 1.4 we show that the answer remains negative even in the setting of count- able linear groups. This contrasts nicely with the prior results of [GG14, GMS15] that show that the answer to the same question is positive for linear groups when the permu- tational characteristic of Γ is not 2; or in other words under the additional assumption that involutions in Γ fix a point. Splitting implies a tame, algebraic, structure theory. In particular with every split sharply 2-transitive group Γ one can associate a near field N, which is by definition a

publication date

  • January 1, 2016