  We study mixing properties of epimorphisms of a compact connected
finite-dimensional abelian group $X$. In particular, we show that a set $F$,
$|F|>\dim X$, of epimorphisms of $X$ is mixing iff every subset of $F$ of
cardinality $(\dim X)+1$ is mixing. We also construct examples of free
nonabelian groups of automorphisms of tori which are mixing, but not mixing of
order 3, and show that, under some irreducibility assumptions, ergodic groups
of automorphisms contain mixing subgroups and free nonabelian mixing
subsemigroups.
