On one question of B. Amberg
In the case where a group $G$ is the product $G = AB$ of Abelian subgroups $A$ and $B$, one of which has і finite 0-rank, it is proved that the Fitting subgroup $F$ and the Hirsch - Plotkin radical $R$ admit the lecompositions $F = (F \bigcap A)(F \bigcap B)$ and $R = (R \bigcap A)(R \bigcap B)$, respectively. This gives the affinitive answer to B. Amberg's question.
English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 4, pp 488-491.
Citation Example: Sysak Ya. P. On one question of B. Amberg // Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 457–461.