The maximal subgroups of the Baby Monster. I (Q1279809)

The maximal subgroups of the Baby Monster simple group are described. This completes the preceeding investigations of the author [Invent. Math. 89, 197-218 (1987; Zbl 0622.20007), Bull. Lond. Math. Soc. 25, No. 1, 23-28 (1993; Zbl 0737.20008), and Arch. Math. 61, No. 6, 497-507 (1993; Zbl 0823.20019)]. The list of 22 maximal subgroups in the ATLAS is therefore augmented by eight new maximal subgroups. The author presents his general strategy of the proof together with brief descriptions of computations and results. The full details will appear in part II of this paper.