Research and Innovation Articles
Published 2010-06-09
Keywords
- Sumset,
- p-group,
- additive number theory
How to Cite
Mutis, W. F., Benavides, F. A., & Castillo, J. H. (2010). Small Sumsets in Finite p-groups. Revista Integración, Temas De matemáticas, 28(1), 79–83. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2061
Abstract
In this paper we present an explicit formula for the functionμG(r, s) = min |A·B|, where A and B are subsets of a finite p-group G with|A| = r, |B| = s and 1 r, s |G|.
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References
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[2] Eliahou S., and Kervaire M., Bounds on the minimal sumsets size function in groups, J. Number Theory, 4 (2007), 503–511. [3] Eliahou S., and Kervaire M., Sumsets in vector spaces over finite fields, J. Number
Theory, 71 (1998), 12–39. MR1631038 (99d:11020)
[4] Eliahou S., and Kervaire M., Minimal sumsets in infinite abelian groups, J. Algebra, 287 (2005), 449–457. MR2134154 (2006c:11018)
[5] Eliahou S., and Kervaire M., Sumsets in dihedral groups, European J. Combin., 27 (2006), 617–628. MR2215221 (2007a:11027)
[6] Kemperman J.H.B., On complexes in a semigroup, Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math., 18 (1956), 247–254. MR0079005 (18,14a)