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

2023/12/28 by Amelio, Marco, André, Simon, Tent, Katrin
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2312.16992

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^ℵ₀ many pairwise non-isomorphic countable non-split sharply 2-transitive groups in any sufficiently large characteristic.

Related

• Non-split sharply 2-transitive groups of bounded exponent
• Non-split linear sharply 2-transitive groups
• Simple sharply 2-transitive groups
• Sharply 2-transitive groups in characteristic 0
• Addendum to Sharply 2-transitive groups of characteristic~0 [arXiv:1604.00573]