# An addition theorem for Abelian groups of order pq

@inproceedings{Diderrich1975AnAT, title={An addition theorem for Abelian groups of order pq}, author={George T. Diderrich}, year={1975} }

Abstract Let G be a group written additively and let A denote a set of nonzero elements of G . The smallest integer n such that every element g in G occurs as a sum of distinct elements over any set A with | A | ≥ n is called the critical number of G , written c ( G ). In this paper, the existence of c ( G ) is proved, lower bounds are established for certain groups, and p + q − 2 ≤ c ( G ) ≤ p + q − 1 is proved for Abelian groups of order pq .

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