Maximal Overgroups of Singer Elements in Classical Groups

Presentations of finite simple groups: profinite and cohomological approaches

“…Note that by Lemma 3.8, N ). It now follows by the main result of [9] (based on [24]) that H = N, zN z −1 . Apply [23,Lemma 4] …”

Chiral polyhedra and finite simple groups

“…When x is a Singer subgroup (i.e. the intersection with G of a cyclic subgroup generated by a Singer cycle of P SL(V )), this follows from the main theorem of [3]. This covers the cases where G = L n (q), U n (q) with n odd, P Sp 2m (q) and P Ω Table 4.…”

“…x := (1,14,17,21,10,5,2,16,18,12,8) (3,6,19,22,15,9,20,23,4,7,11), y := (1,8,6,10,21,22,19,12,11,7,4,5,3,18,9) (2,23,20,16,13) (14,15,17), and t := xy. The pair x, t satisfies (i)-(iii) of Theorem 1.1.…”

Overgroups of Cyclic Sylow Subgroups of Linear Groups

“…(b) Other examples: We have that d = 8, e = 6, q = p, A n G S n and (n, p) ∈ {(10, 5), (9,5), (8,3), (7, 5)}. The number of times an isomorphism type of a group appears in a row for the H column is equal to the number of conjugacy classes of that isomorphism type for H in G. We have the following data in each case:…”