A new 7-local subgroup of the Monster (Q1101545)

The author gives an independent proof of a result due to the reviewer [J. Aust. Math. Soc., Ser. A 44, No.1, 1-16 (1988; Zbl 0636.20014)], which determines the maximal 7-local subgroups of the Monster up to conjugacy. These are as listed in the `ATLAS of finite groups' [\textit{J. H. Conway} et al., 1985; Zbl 0568.20001] except that there is a further (so-called ``new'') subgroup of shape 7 2: SL\({}_ 2(7)\). The reviewer (loc. cit.) has also determined the maximal 3-local and 5-local subgroups of the Monster.