Abstract
A finitely supported measure yt on an l.c.a. group is said to be extremal if II = 11 1 (# SUpp t,) 12. If yt is an extremal measure and E is the support of ,t, it follows that the Sidon constant of E is (# E)'/2, in which case E is also said to be extremal. Our results are these. (1) An independent union of m cosets of a finite subgroup H of G is extremal if and only if (essentially) m divides #H. (2) Not all extremal subsets of abelian groups have the form described in (1). (3) For any group (abelian or not), the Sidon constant of that group is at least (.8)(# G)'/3.
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