Chains of subgroups in groups of Lie type I

Chains of Subgroups in Groups of Lie Type Ii

“…The result is trivial for 2 B 2 (2), since it is solvable. For 2 B 2 (q), q > 2, and for 2 F i {q), the result follows from [7,Theorem 1].…”

“…We next turned to groups of Lie type and obtained the following result. THEOREM 1.4 [7]. Let G r (k) be a finite simple group of Lie type over the field k of characteristic 2.…”

Almost simplep-obstructions in odd characteristic lie type groups∗

“…Using the Atlas ([lo]), one can determine the length of 24 of the 26 sporadic simple groups (the length of the "monster" and the 'baby monster" are not known). For the infinite classes, results have been obtained by Cameron, Solomon and Turull (Theorem 1, [8]) for the Alternating groups, by Solomon and Turull for even characteristic Lie type groups (Theorem 1, [15]) and recently by this author for Lie type groups in odd characteristic p, p < 29 (Theorem 1.2, (41).…”

“…With the exception of L5(2) and PR;(2), we have 6 > 28, which forces t(U) 2 7(26) = 182 > 45 > ! (M) (45 coming from explicit computation via Theorem 1 of [15]). If F * ( M ) E L5(2), 6 = 15 and we obtain If F * ( M ) 2 PR$(2), then 6 > 8 and we may assume G is isomorphic to one of the following groups: L8jpk)), u~(~~) , PSpg(pC), PR9(pk) pfi8+(pk), or PR;(pk).…”

“…In [15] and 141, a complete determination of ail groups of hypel.bolic length (p 5 29) is achieved. Theorem 1.1 in this note serves as the initial step in this classification in the odd characteristic case ( [4]).…”