A NOTE ON KNESER’S THEOREM

Xuesheng Chen (P. R. China) and Pingzhi Yuan (P. R. China)

Abstract

In this note, we obtain a result on the cardinality of the finite subset sums of abelian groups, which improves upon a result of Gao. Furthermore, we prove that the beautiful theorem of Kneser and the well known result of Kemperman and Scherk can be deduced easily from the result here. Finally, we give an application of the result.

Keywords and phrases: Kneser’s theorem, abelian group, cardinality.