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Published online by Cambridge University Press: 01 September 1999
Let A be a subset of an abelian group G. The subset sum of A is the set [sum ](A) = {[sum ]x∈T[mid ]T⊂A}. We prove the following result. Let S be a generating subset of an abelian group G such that 0∉S and 14[les ][mid ]S[mid ]. Then one of the following conditions holds.
(i) [mid ][sum ](S)[mid ][ges ]min([mid ]G[mid ] −3, 3[mid ]S[mid ]−3).
(ii) There is an x∈S such that S[setmn ]{x} generates a proper subgroup of order less than (3[mid ]S[mid ]−3)/2.
As a consequence, we obtain the following open case of an old conjecture of Diderrich. Let q be a composite odd number and let G be an abelian group of order 3q. Let S be a subset of G with cardinality q+1. Then every element of G is the sum of some subset of S.
