On weakly factorizable groups. (Q1886131)

By definition a subgroup \(M\) of a group \(G\) is called complemented in \(G\) if there is a subgroup \(K\) of \(G\) such that \(G=MK\) and \(M\cap K=1\). A group \(G\) is called completely factorizable if each of its subgroups is complemented in \(G\). These groups are described by \textit{N. V. Chernikova} [Mat. Sb., Nov. Ser. 39(81), 273-292 (1956; Zbl 0071.02202)]. As a result if each subgroup of a completely factorizable group \(G\) has a normal complement in a larger subgroup, then the group \(G\) is completely factorizable. Motivated by this result, the author defines a larger class of factorizable groups, namely weakly factorizable groups. A group \(G\) is called weakly factorizable if each of its proper subgroups is complemented in some larger subgroup. Although the description of all the weakly factorizable groups is not given in the present paper, it is proved that the dihedral group of order \(2n\), where \(2n\) is a square free number, and the Sylow subgroups of some classical groups, are weakly factorizable.