Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424380 | European Journal of Combinatorics | 2013 | 7 Pages |
Abstract
One sees that, as a corollary of Kneser's theorem, any finite non-empty subset A of an abelian group G=(G,+) with |A+A|â¤(2âε)|A| can be covered by at most 2εâ1 translates of a finite group H of cardinality at most (2âε)|A|. Using some arguments of Hamidoune, we establish an analogue in the noncommutative setting. Namely, if A is a finite non-empty subset of a nonabelian group G=(G,â ) such that |Aâ A|â¤(2âε)|A|, then A is either contained in a right-coset of a finite group H of cardinality at most 2ε|A|, or can be covered by at most 2εâ1 right-cosets of a finite group H of cardinality at most |A|. We also note some connections with some recent work of Sanders and of Petridis.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Terence Tao,