Abstract: | An n-subsetD of a group G of order
is called an affine difference set of G relativeto a normal subgroup N of G of order
if the list of differences
containseach element of G-N exactly once and no elementof N. It is a well-known conjecture that if Dis an affine difference set in an abelian group G,then for every prime p, the Sylow p-subgroupof G is cyclic. In Arasu and Pott 1], it was shownthat the above conjecture is true when
. In thispaper we give some conditions under which the Sylow p-subgroupof G is cyclic. |