Please use this identifier to cite or link to this item: https://doi.org/10.1006/jnth.2002.2793
Title: A generalization of an addition theorem of Kneser
Authors: Hou, X.-D.
Leung, K.H. 
Xiang, Q.
Keywords: Finite field
Kneser's theorem
The Cauchy-Davenport theorem
The Dyson e-transform
Issue Date: 1-Nov-2002
Source: Hou, X.-D., Leung, K.H., Xiang, Q. (2002-11-01). A generalization of an addition theorem of Kneser. Journal of Number Theory 97 (1) : 1-9. ScholarBank@NUS Repository. https://doi.org/10.1006/jnth.2002.2793
Abstract: A theorem of Kneser states that in an abelian group G, if A and B are finite subsets in G and AB = {ab:a ε A,b ε B}, then AB ≥ A + B - H(AB) where H(AB) = {g ε G: g(AB) = AB}. 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. © 2002 Elsevier Science (USA).
Source Title: Journal of Number Theory
URI: http://scholarbank.nus.edu.sg/handle/10635/102653
ISSN: 0022314X
DOI: 10.1006/jnth.2002.2793
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