A generalization of the Cauchy-Davenport Theorem to arbitrary finite groups was suggested by Karolyi and proved independently by Karolyi and Wheeler. Here we give a short proof of the following small extension of this result (which also applies to infinite groups): If A, B are finite nonempty subsets of a (multiplicatively written) group G then |AB| min{p(G), |A| + |B| 1} where p(G) denotes the smallest order of a nontrivial finite subgroup of G, or 1 if no such subgroups exist.
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机译：Karolyi提出了Cauchy-Davenport定理对任意有限群的概括，并通过Karolyi和Wheeler独立证明。在这里，我们给出了以下延长此结果的小额延长（这也适用于无限组）：如果a，b是（乘以写的）组g的有限非空的子集| ab |最小{P（g），| A | + | B | 1}其中p（g）表示如果没有存在这样的子组，则不表示为g，或1的非活动有限子组的最小顺序。
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