On Chernikovp-groups

We investigate extensions of divisible Abelianp-groups with minimality condition by means of a finitep-groupH and establish the conditions under which the problem of describing all nonisomorphic extensions of this sort is wild. All the nonisomorphic Chernikovp-groups are described whose factor-group with respect to the maximum divisible Abelian subgroup is a cyclic group of orderp ^s ,s≤2. Uzhgorod University, Uzhgorod. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 291–304, March, 1999.