Sufficient conditions for the almost layer finiteness of groups

We prove a theorem that describes almost layer-finite groups in the class of conjugatively biprimitive-finite groups. Computer Center of the Siberian Division of the Russian Academy of Sciences, Krasnoyarsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 472–485, April, 1999.