Theorems of the type of Cutler for abelian p-groups

Suppose G and H are abelian p-groups. It is shown that if G and H are quasi- isomorphic then G is (a) summable or (b) ?-summable or (c) p?+m-projective, m ? IN0 = IN ?{0} or (d) a strong ?-elongation of a totally projective (respectively summable) group by a p?+m-projective group, m ? IN0 = IN ?{0} or (e) thick if and only if so is H. These ?ve independent claims comple- mented results of this type due to Cutler (appeared in Pac. J. Math., 1966) and are supplements to our recent results (published in Proc. Indian Acad. Sci.-Math. Sci., 2004) too.