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A Generalization of an Addition Theorem of Kneser

✍ Scribed by Xiang-Dong Hou; Ka Hin Leung; Qing Xiang

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 109 KB
Volume: 97
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2002.2793

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✦ Synopsis

A theorem of Kneser states that in an abelian group G; if A and B are finite subsets in G and AB ¼ fab : a 2 A; b 2 Bg; then jABj5jAj þ jBj À jHðABÞj where HðABÞ ¼ fg 2 G : gðABÞ ¼ ABg: Motivated by the study of a problem in finite fields, we prove an analogous result for vector spaces over a field E in an extension field K of E: Our proof is algebraic and it gives an immediate proof of Kneser's Theorem.

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