On one question of B. Amberg

In the case where a group G is a productG=AB of Abelian subgroupsA andB one of which has a finite 0-rank, we prove that the Fitting subgroupF and the Hirsch-Plotkin radicalR admit the decompositionsF=(F A)(F B) andR=(RA)(R B), respectively. This gives the affirmative answer to one question of B. Amberg.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 457–461, April, 1994.This paper was supported by the Ukrainian State Foundation on Science and Technology.