Non-split sharply 2-transitive groups of odd positive characteristic

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 $2^{{\aleph }_0}$ many pairwise non-isomorphic countable non-split sharply 2-transitive groups in any sufficiently large characteristic.

arXiv admin note: text overlap with arXiv:1311.0855 by other authors