Finite groups determined by an inequality of the orders of their elements. (Q2915411)

The author considers finite groups \(G\) satisfying the property \(o(xy)\leq\max\{o(x),o(y)\}\), \(\forall x,y\in G\) and denoted by \(\mathrm{CP}_2\) groups. It is not difficult to prove that \(\mathrm{CP}_2\)-groups is a subclass of CP groups [see \textit{G.~Higman}, J. Lond. Math. Soc. 32, 335-342 (1957; Zbl 0079.03204)]. CP groups are also called EPPO-groups [see \textit{W.~J.~Shi} and \textit{W.~Z.~Yang}, J. Yunnan Ed. Coll. 1986, No.~1, 2-10 (1986)], and their structure may be obtained from that paper. In the end of this paper, the author poses the following problem: give a precise description of finite \(p\)-groups contained in \(\mathrm{CP}_2\). This is a difficult problem.