A structural criterion for the existence of infinite central Λ(𝑝) sets

Hare, Kathryn E.; Wilson, David C.

doi:10.1090/S0002-9947-1993-1157613-2

A structural criterion for the existence of infinite central $\Lambda (p)$ sets
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by Kathryn E. Hare and David C. Wilson PDF

Trans. Amer. Math. Soc. 337 (1993), 907-925 Request permission

Abstract:

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

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