Sums of lengtht in Abelian groups |
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Authors: | George T Diderrich |
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Institution: | (1) 2973 N. Cramer St., 53211 Milwaukee, Wisconsin, U. S. A. |
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Abstract: | LetG be an Abelian group written additively,B a finite subset ofG, and lett be a positive integer. Fort≦|B|, letB
t denote the set of sums oft distinct elements overB. Furthermore, letK be a subgroup ofG and let σ denote the canonical homomorphism σ:G→G/K. WriteB
t (modB
t) forB
tσ and writeB
t (modK) forBσ. The following addition theorem in groups is proved. LetG be an Abelian group with no 2-torsion and letB a be finite subset ofG. Ift is a positive integer such thatt<|B| then |B
t (modK)|≧|B (modK)| for any finite subgroupK ofG. |
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Keywords: | |
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