Submission date: 28 December 2023

Abstract:

It is well-known that every sharply 2-transitive group of characteristic 3 splits. Here we construct the first examples of non-split sharply 2-transitive groups in odd positive characteristic p, for sufficiently large primes p. Furthermore, we show that any group without 2-torsion can be embedded into a non-split sharply 2-transitive group of characteristic p for all sufficiently large primes p, yielding 2^{ℵ_0} many pairwise non-isomorphic countable non-split sharply 2-transitive groups in any sufficiently large characteristic.

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Full text arXiv 2312.16992: pdf, ps.