We classify the compact, connected groups which have infinite central
Λ
(
p
)
\Lambda (p)
sets, arithmetically characterize central
Λ
(
p
)
\Lambda (p)
sets on certain product groups, and give examples of
Λ
(
p
)
\Lambda (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.