Mathematics & Physics 2015, 8(4), 377–384 УДК 519.41/47 Shunkov Groups with the Minimal Condition for Noncomplemented Abelian Subgroups Nikolai S. Chernikov∗ Institute of Mathematics National Academy of Sciences of Ukraine Tereschenkivska, 3, Kyiv-4, 01601 Ukraine Received 10.09.2015, received in revised form 21.09.2015, accepted 02.11.2015 In the present paper, we give a complete exhaustive description of the pointed out Shunkov groups. <...> DOI: 10.17516/1997-1397-2015-8-4-377-384 Introduction A great many deep and bright results are connected with groups, satisfying various minimal conditions, and with groups, having wide systems of complemented subgroups (see, for instance, [1–7]). <...> The present paper is devoted to the Shunkov groups with the minimal condition above. <...> Below p and q are always primes; min−ab, min−abc, min−p and min−p′ are the minimal conditions respectively for abelian, abelian noncomplemented, for p- and p′-subgroups. <...> Remind that the group G is called Shunkov, if for any its finite subgroup K, every subgroup of the factor group NG(K)/K, generated by two conjugate elements of prime order, is finite (V. D. Mazurov, 1998). <...> The class of Shunkov groups is wide and includes, for instance, binary finite groups, 2-groups. <...> The known Suchkova–Shunkov Theorem [8] (see also [4, Theorem 4.5.1]) asserts: The Shunkov group with min−ab is Chernikov. <...> Further, remind that the subgroup H of the group G is called complemented in G, if for some subgroup K of G, G = HK and H∩K = 1; K is called a complement of H in G. The group G is called completely factorizable, if every its subgroup is complemented in it (N. V. Chernikova [9]). <...> The fundamental N. V. Chernikova’s Theorem [9, 10] (see also, for instance, [1, Theorem 7.2]) gives an exhaustive description of completely factorizable groups and asserts: The group G ̸= 1 is completely factorizable iff G = AB where A is a direct product of normal subgroups of prime orders of G and B is a direct product of subgroups of prime orders or B = 1; in particular, the p-group G is completely <...>