Non-Split Sharply 2-Transitive Groups of Odd Characteristic

Explore the construction of non-split sharply 2-transitive groups in odd characteristic through this 11-minute mathematical lecture. Learn about the historical context of this open problem, which remained unsolved until recent breakthroughs by Rips, Segev, and Tent in 2017 and 2019. Understand the concept of sharply 2-transitive groups and their associated characteristics, which can be either 0 or a positive prime number. Discover how previous examples were limited to characteristic 2 and characteristic 0, leaving odd characteristics as an open question. Follow the speaker's outline of an adapted construction method that extends the characteristic 0 approach to build examples of non-split sharply 2-transitive groups in odd characteristic using geometric small cancellation techniques. Gain insight into this collaborative research conducted with Simon André and Katrin Tent that addresses a significant gap in the understanding of these mathematical structures.