54 research outputs found
Lie rank in groups of finite Morley rank with solvable local subgroups
We prove a general dichotomy theorem for groups of finite Morley rank with
solvable local subgroups and of Pr\"ufer p-rank at least 2, leading either to
some p-strong embedding, or to the Pr\"ufer p-rank being exactly 2
Involutive automorphisms of groups of finite Morley rank
We classify a large class of small groups of finite Morley rank:
-groups which are the infinite analogues of Thompson's
-groups. More precisely, we constrain the -structure of groups of finite
Morley rank containing a definable, normal, non-soluble,
-subgroup
Simple groups of Morley rank 5 are bad
By exploiting the geometry of involutions in -groups of finite
Morley rank, we show that any simple group of Morley rank is a bad group
all of whose proper definable connected subgroups are nilpotent of rank at most
. The main result is then used to catalog the nonsoluble connected groups of
Morley rank
Rank 3 Bingo
We classify irreducible actions of connected groups of finite Morley rank on
abelian groups of Morley rank 3
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