The author studies the natural mappings of the relative Wall groups fo
r the imbedding Zpi --> Z2pi that occur in a two-row diagram, in the c
ase of finite abelian 2-groups. It is shown that in this case the diag
ram splits into a direct sum of a certain number of four different dia
grams. The results are applied to the study of mappings of surgery obs
truction groups.