An identification of the Monster group. (Q2269654)

Let \(G\) be a finite group. In 1989, \textit{R. L. Griess} jun., \textit{U. Meierfrankenfeld} and \textit{Y. Segev} proved that the Monster group is determined by two special centralizers of involutions in \(G\) [see Ann. Math. (2) 130, No. 3, 567-602 (1989; Zbl 0691.20014)]. In this paper, the authors find such involutions in \(G\) and prove that the Monster group may be identified from two of the 3-local subgroups in \(G\).