2025/09/15 by Amelio, Marco
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2509.11958
We construct here the first known examples of non-split sharply 2-transitive groups of bounded exponent in odd positive characteristic for every large enough prime p ≡ 3 \pmod4. In fact, we show that there are countably many pairwise non-isomorphic countable non-split sharply 2-transitive groups of characteristic p for each such p. Furthermore, we construct non-periodic non-split sharply 2-transitive groups (of these same characteristics) with centralizers of involutions of bounded exponent. As a consequence of these results, we answer two open questions about sharply 2-transitive and 2-transitive permutation groups. The constructions of groups as announced rely on iteratively applying (geometric) small cancellation methods in the presence of involutions. To that end, we develop a method to control some small cancellation parameters in the presence of even-order torsion.