Maximal Cofinitary groups are considered close relatives to
the maximal
almost disjoint families. However, while there are no analytic mad
families, there
are Borel maximal cofinitary groups. Since every Borel maximal
cofinitary group
is of size continuum, it is of interest to ask, what the complexities of
maximal
cofinitary groups of cardinality strictly below the continuum can be. It
is known,
that in the constructible universe, there are co-analyitc Cohen
indestructible
maximal cofinitary groups, which gives rise to the existence of a
co-analytic maximal
cofinitary group of size aleph_1 in a model of large continuum.

In this talk, we will discuss the existence of a nicely definable
maximal cofinitary
group of size strictly between aleph_1 and c (the size of the continuum), which is
of minimal
projective complexity.