Results concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards and Ross. A notion of test family is introduced and is used to give necessary conditions for a set to be lacunary. Using this, it is shown that (2) has no infinite p-Sidon sets for 1 ≤p<2.