  We consider ten linear rank inequalities, which always hold for ranks of
vector subspaces, and look at them as group inequalities. We prove that groups
of order pq, for p,q two distinct primes, always satisfy these ten group
inequalities. We give partial results for groups of order $p^2q$, and find that
the symmetric group $S_4$ is the smallest group that yield violations, for two
among the ten group inequalities.
