THE STRONGLY HOPFIAN ABELIAN GROUPS

Let A be an abelian group, A is said strongly hopan if for all f 2 End(A) we have the chain Ker(f) Ker(f 2 ) Ker(f 3 ) Ker(f 4 ) is stationary. In this paper, we characterize strongly hopan abelian group in the class of torsion abelian group. After we show that the p-component of strongly hopan abelian group is strongly hopan. But for the torsion part, we construct strongly hopan abelian group whose the torsion part is not strongly hopan.