Optimally small sumsets in finite abelian groups.

DOI10.1016/S0022-314X(03)00060-XzbMath1043.11021MaRDI QIDQ1398954

Shalom Eliahou, Alain Plagne, Michel A. Kervaire

Publication date: 7 August 2003

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Cauchy-Davenport theoremKneser theoremInitial segmentSumset

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Finite abelian groups (20K01) Inverse problems of additive number theory, including sumsets (11P70)

Related Items (24)

Sumsets in dihedral groups. ⋮ On Sums of Generating Sets in ℤ₂ⁿ ⋮ Direct and inverse problems for restricted signed sumsets in integers ⋮ The small sumsets property for solvable finite groups ⋮ An inverse theorem for the restricted set addition in Abelian groups. ⋮ On the minimum size of restricted sumsets in cyclic groups ⋮ Some results on minimal sumset sizes in finite non-Abelian groups. ⋮ Partitions of nonzero elements of a finite field into pairs ⋮ Sumsets in dicyclic groups Q _{4 n} and U _m,n ⋮ BOUNDS ON THE MINIMAL SUMSET SIZE FUNCTION IN GROUPS ⋮ Minimum product sets sizes in nonabelian groups. ⋮ The Freiman-Ruzsa theorem over finite fields ⋮ The minimum size of signed sumsets ⋮ Minimal sumsets in finite solvable groups. ⋮ Old and new formulas for the Hopf-Stiefel and related functions ⋮ Minimal sumsets in infinite Abelian groups. ⋮ Planar additive bases for rectangles ⋮ On the minimum size of signed sumsets in elementary abelian groups ⋮ Minimum product set sizes in nonabelian groups of order \(pq\). ⋮ THE ISOPERIMETRIC METHOD IN NON-ABELIAN GROUPS WITH AN APPLICATION TO OPTIMALLY SMALL SUMSETS ⋮ Unnamed Item ⋮ Growth in Infinite Groups of Infinite Subsets ⋮ A compactness argument in the additive theory and the polynomial method. ⋮ Some extensions of the Cauchy-Davenport theorem

Cites Work

• Unnamed Item
• Orthogonal pairings of Euclidean spaces
• Sumsets in vector spaces over finite fields
• Sums in the grid
• Additive number theory sheds extra light on the Hopf-Stiefel \(\circ\) function.
• Abschätzung der asymptotischen Dichte von Summenmengen
• On the Addition of Residue Classes
• Two addition theorems

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