We define the notion of mock hyperbolic reflection spaces and use it to study
Frobenius groups. These turn out to be particularly useful in the context of
Frobenius groups of finite Morley rank including the so-called
bad groups. We show
that connected Frobenius groups of finite Morley rank and odd type with nilpotent
complement split or interpret a bad field of characteristic zero. Furthermore, we show
that mock hyperbolic reflection spaces of finite Morley rank satisfy certain rank
inequalities, implying, in particular, that any connected Frobenius group of
odd type and Morley rank at most ten either splits or is a simple nonsplit
sharply
-transitive
group of characteristic
of Morley rank
or
.
Keywords
Frobenius groups, sharply 2-transitive groups, groups of
finite Morley rank, Bachmann geometries
