Simple groups of Morley rank 5 are bad

2017/07/07 by Adrien Deloro, Deloro, Adrien, Joshua Wiscons +1
Mathematics · #20F11 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO #msc:20F11

paper · pdf · doi:10.48550/arxiv.1707.02057

arxiv created 2017/07/07 · arxiv updated 2017/07/10

Abstract

By exploiting the geometry of involutions in N_∘^∘-groups of finite Morley rank, we show that any simple group of Morley rank 5 is a bad group all of whose proper definable connected subgroups are nilpotent of rank at most 2. The main result is then used to catalog the nonsoluble connected groups of Morley rank 5.

Related

• Groups of Morley rank 4
• Linear groups of finite Morley rank
• Bad Groups
• Small groups of finite Morley rank with involutions
• Bad groups in the sense of Cherlin