Kemperman结构定理之推广

An Extension of Kemperman Structure Theorem

设G为任意Abelian群,A,B■G为有限非空子集．在1960年,Kemperman给出了满足|A+B|=|A|+|B|-1的对(A,B)的结构完全递归描述．本文探讨满足|A+B|=|A|+|B|+k(其中k为整数,且k■-1)的那些对(A,B),并推广了Kemperman结构定理．

In this paper, we investigate the structure of the those pairs（A, B） of finite subsets of an Abelian group satisfying ｜A ＋ B｜ = ｜A｜ ＋ ｜B｜ ＋ κ （κ ≥ -1）, and extend the Kemperman structure theorem.