  We consider distinction of representations in the context of $p$-adic Galois
symmetric spaces. We provide new sufficient conditions for distinction of
parabolically induced representations in terms of similar conditions on the
inducing data and deduce a characterization for distinction of representations
parabolically induced from cuspidal. We explicate the results further for
classical groups and give several applications, in particular, concerning the
preservation of distinction via Langlands functoriality. We relate our results
with a conjecture of Dipendra Prasad.
