TY - JOUR

T1 - Perfect sumsets in finite Abelian groups

AU - Blokhuis, A.

AU - Wilbrink, H.A.

AU - Sali, A.

PY - 1995

Y1 - 1995

N2 - We prove that if G is a finite abelian group of odd order n and A G is of size a such that for every g e G there exist u, v e A with g = u + v, then n = [(a - 1)2 + 1]/2 if a is even and n = [(a - 1)2 + 2]/2 if a is odd. We show that equality occurs if and only if n e {3, 5, 9, 13, 25, 243}.

AB - We prove that if G is a finite abelian group of odd order n and A G is of size a such that for every g e G there exist u, v e A with g = u + v, then n = [(a - 1)2 + 1]/2 if a is even and n = [(a - 1)2 + 2]/2 if a is odd. We show that equality occurs if and only if n e {3, 5, 9, 13, 25, 243}.

U2 - 10.1016/0024-3795(95)00232-G

DO - 10.1016/0024-3795(95)00232-G

M3 - Article

VL - 226-228

SP - 47

EP - 56

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -