Abstract
Let
G be an abelian
group of order
n. The
critical number
c(
G) of
G is the smallest
s such that the subset sums
set
$
{\left| S \right|} \geqslant \frac{{n + 11}}
{4}
$
{\left| S \right|} \geqslant \frac{{n + 11}}
{4}
for which
(S) =G are also characterized when
n
183, the smallest prime
p dividing
n is odd and
n/p is composite. Finally we
obtain a necessary and sufficient condition for the equality
(G)=G
to hold when |S|n/(p+2)+p, where p5, n/p is composite and
n15p2. Mathematics Subject
Classification (2000): 11A75 - 20K01
* Work partially supported by the Spanish Research
Council under grant TIC2000-1017
Work partially supported by the Catalan Research
Council under grant 2000SGR00079