Article
Optimally Small Sumsets in Groups, I. the Supersmall Sumsets Property, the Μ(k) and the Ν(k) Functions G G
Authors
Abstract
We introduce the generalized supersmall sumsets property and prove that it holds for all solvable groups. As applications, using this tool to- gether with a generalized version of Kneser’s theorem, we establish, for G Abelian, an explicit formula for the generalized µ(k) functions in terms of the cardinalities G of the finite subgroups of G and we study the ν(k) functions, which count the G minimal cardinality of a sumset containing an element with a single representa- tion.
Keywords
group, Abelian, cyclic, solvable, sumset.
Citation
Plagne, A. (2006). Optimally small sumsets in groups, i. the supersmall sumsets property, the μ(k) and the ν(k) functions g g. Uniform Distribution Theory, 1(1), 27–44.
A. Plagne, “Optimally small sumsets in groups, i. the supersmall sumsets property, the μ(k) and the ν(k) functions g g,” Uniform Distribution Theory, vol. 1, no. 1, pp. 27–44, 2006.
Plagne A. Optimally small sumsets in groups, i. the supersmall sumsets property, the μ(k) and the ν(k) functions g g. Uniform Distribution Theory. 2006;1(1):27–44.
Plagne, A. (2006), ‘Optimally small sumsets in groups, i. the supersmall sumsets property, the μ(k) and the ν(k) functions g g’, Uniform Distribution Theory, 1(1), pp. 27–44.
Plagne, Alain. “Optimally Small Sumsets in Groups, I. the Supersmall Sumsets Property, the Μ(k) and the Ν(k) Functions G G.” Uniform Distribution Theory, vol. 1, no. 1, 2006, pp. 27–44.
Plagne, Alain. “Optimally Small Sumsets in Groups, I. the Supersmall Sumsets Property, the Μ(k) and the Ν(k) Functions G G.” Uniform Distribution Theory 1, no. 1 (2006): 27–44.
Export citation
Published by: Engineering Journals
