On one question of B. Amberg

Abstract

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.