The maximal subgroups of the Steinberg triality groups \(3D_ 4(q)\) and their automorphism groups
The author determines the maximal subgroups of the finite Steinberg groups \(3D_ 4(q)\), and of their automorphism groups. This involves embedding \(3D_ 4(q)\) in \(O\) \(+_ 8(q\) 3) and using the associated geometry of triality to investigate the embeddings of maximal subgroups in \(3D_ 4(q)\). Much use is made of the author's earlier paper on the maximal subgroups of \(O\) \(+_ 8(q)\) [J. Algebra 110, 173-242 (1987; Zbl 0623.20031)], which is also used in his determination of the maximal subgroups of \(G_ 2(q)\) for q odd, and the Ree groups \(2G_ 2(q)\) [ibid. 117, No.1, 30-71 (1988)]. As is usual in this area, this work relies on the classification of finite simple groups.
scientific article; zbMATH DE number 4045996