A generation theorem for groups of finite Morley rank

TL;DR

This paper extends classification results for large simple groups of finite Morley rank of odd type, focusing on the uniqueness cases and broadening the scope to L*-groups, including specific groups like PSp_4 and G_2.

Contribution

It introduces a generation theorem for groups of finite Morley rank, extending prior results to include new groups and the broader L*-group setting.

Findings

Extended classification to include PSp_4 and G_2 groups.

Analyzed the structure of large simple groups of finite Morley rank.

Broadened the scope from K*-groups to L*-groups.

Abstract

We deal with two forms of the "uniqueness cases" in the classification of large simple $K^*$-groups of finite Morley rank of odd type, where large means the $m_2(G)$ at least three. This substantially extends results known for even larger groups having \Prufer 2-rank at least three, to cover the two groups $\PSp_4$ and $\G_2$. With an eye towards distant developments, we carry out this analysis for $L^*$-groups which is substantially broader than the $K^*$ setting.