  The main result of the present paper is that $\mathfrak a_g$, the minimal
size of maximal cofinitary group, can be of countable cofinality. To prove this
we define a natural poset for adding a maximal cofinitary group of a given
cardinality, which enjoys certain combinatorial properties allowing it to be
used within a similar template forcing construction. Additionally we obtain
that $\mathfrak a_p$, the minimal size of a maximal family of almost disjoint
permutations, and $\mathfrak a_e$, the minimal size of a maximal eventually
different family, can be of countable cofinality.
