  We provide new examples of the asymptotic counting for the number of subsets
on groups of given size which are free of certain configurations. These
examples include sets without solutions to equations in non-abelian groups, and
linear configurations in abelian groups defined from group homomorphisms. The
results are obtained by combining the methodology of hypergraph containers
joint with arithmetic removal lemmas. As a consequence, random counterparts are
presented as well.
