- 18 Downloads
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.
KeywordsFinite Group Cyclic Group Irreducible Component Minimality Condition Cyclic Extension
Unable to display preview. Download preview PDF.
- 1.S. N. Chernikov,Groups with Given Properties of the System of Subgroups [in Russian], Nauka, Moscow (1980).Google Scholar
- 2.A. G. Kurosh,Group Theory [in Russian], Nauka, Moscow (1967).Google Scholar
- 3.D. J. S. Robinson,Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972).Google Scholar
- 5.B. Hartley, “A dual approach to Chernikov modules,”Math. Proc. Cambridge Phil. Soc., 215–239 (1977).Google Scholar
- 16.P. M. Gudivok,Integer Representations of Finite Groups [in Russian], Uzhgorod University, Uzhgorod (1978).Google Scholar