Difference bases in finite Abelian groups

A subset B of a group G is called a difference basis of G if each element g is an element of G can be written as the difference g = ab(-1) of some elements a, b is an element of B. The smallest cardinality vertical bar B vertical bar of a difference basis B subset of G is called the difference size of G and is denoted by Delta[G]. The fraction partial derivative[G] := Delta[G]/root vertical bar G vertical bar is called the difference characteristic of G. Using properties of the Galois rings, we prove recursive upper bounds for the difference sizes and characteristics of finite Abelian groups. In particular, we prove that for a prime number p >= 11, any finite Abelian p-group G has difference characteristic partial derivative[G] < root p-1/root p-3 . sup(k is an element of N) partial derivative[C-pk] < root 2 . root p-1/root p-3. Also we calculate the difference sizes of all Abelian groups of cardinality less than 96.