On a partition analog of the Cauchy-Davenport theorem

Let < InlineEquation > < EquationSource='tex' > G < /EquationSource > < /InlineEqu ation > be a finite abelian group, and let < InlineEquation > < EquationSource='tex' > n < /EquationSource > < /InlineEqu ation > be a positive integer. From the Cauchy-Davenport Theorem it follows that if < InlineEquation > < EquationSource='tex' > G < /EquationSource > < /InlineEqu ation > is a cyclic group of prime order, then any collection of < InlineEquation > < EquationSource='tex' > n < /EquationSource > < /InlineEqu ation > subsets < InlineEquation > < EquationSource='tex' > A_1,A_2,\ldots,A_n < /EquationS ource > < /InlineEquation > of < InlineEquation > < EquationSource='tex' > G < /EquationSource > < /InlineEqu ation > satisfies < InlineEquation > < EquationSource='tex' > \bigg|\sum_{i=1}n A_i\bigg| \ge \min \bigg\{|G|,\,\sum_{i=1}n |A_i|-n+1\bigg\}. < /EquationSource > < /InlineEquation > M.~Kneser generalized the Cauchy--Davenport Theorem for any abelian group. In this paper, we prove a sequence-partition analog of the Cauchy--Davenport Theorem along the lines of Kneser's Theorem. A particular case of our theorem was proved by J.~E. Olson in the context of the Erdoes--Ginzburg--Ziv Theorem.