Abstract. We classify the compact, connected groups which have infinite central A(p) sets, arithmetically characterize central A(p) sets on certain product groups, and give examples of A(p) sets which are non-Sidon and have unbounded degree. These sets are intimately connected with Figà-Talamanca and Rider's examples of Sidon sets, and stem from the existence of families of tensor product representations of almost simple Lie groups whose decompositions into irreducibles are rank-independent. 1
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