Submission date: 21 July 2021

Abstract:

We investigate the configuration where a group of finite Morley rank acts definably and generically m-transitively on an elementary abelian p-group of Morley rank n, where p is an odd prime, and m ≥ n. We conclude that m=n, and the action is equivalent to the natural action of GL_n(F) on F^n for some algebraically closed field F. This strengthens our earlier result in arXiv:1802.05222, and partially answers two problems posed by Borovik and Cherlin in 2008.

Mathematics Subject Classification: 20F11, 03C60

Keywords and phrases: groups of finite Morley rank, generically transitive group actions

Full text arXiv 2107.09997: pdf, ps.