On the sum of two sets in a group |
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Authors: | John E Olson |
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Institution: | Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 USA |
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Abstract: | Sums C = A + B of two finite sets in a (generally non-abelian) group are considered. The following two theorems are proved. 1. unless C + (?B + B) = C; 2. There is a subset S of C and a subgroup H such that ∣S∣ ≥ ∣A∣ + ∣B∣ ? ∣H∣, and either H + S = S or S + H = S. |
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