Submission date: 12 May 2022

Abstract:

We investigate faithful representations of Alt(n) as automorphisms of a connected group G of finite Morley rank. We target a lower bound of n on the rank of such a nonsolvable G, and our main result achieves this in the case when G is without involutions. In the course of our analysis, we also prove a corresponding bound for solvable G by leveraging recent results on the abelian case. We conclude with an application towards establishing natural limits to the degree of generic transitivity for permutation groups of finite Morley rank.

Mathematics Subject Classification: 03C60, 20F11 (Primary) 20C30 (Secondary) \\

Keywords and phrases:

Full text arXiv 2205.06173: pdf, ps.