Pushing up in Finite Groups

Author: Campbell, Neville Ray

Year: 1979

Degree: Dissertation (Ph.D.)

Advisor: Aschbacher, Michael

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/grvb-z924

Abstract

The main result is a pushing up theorem for L3(2n). Let G be a finite group with F*(G) = O2(G). Suppose there exists a normal subgroup H of G with O2(G) ≤ H such that H/O2(G) has no partial complement in G/O2(G) and G/H is isomorphic to L3(2n). Let T be a Sylow 2-subgroup of G and let X be a maximal 2-local subgroup of G containing H with XH/H a maximal parabolic subgroup of G/H. Let P = O2(X) and E = Ω1 (Z(Q)).

Theorem. If G ≠ {CG(Ω1(Z(T)), NG(J(P))}, then

wither (i) [G,Eα] ≤ E for each automorphism α of P

or (ii) G has exactly one noncentral chief factor within O2(G).

We also derive some new pushing up theorems for L2(2n) which are variations on the results of Baumann, Glauberman and Niles.

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