Atlas: Groups of even and p-type by Inna Korchagina

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Finite Simple Groups, Geometries, Buildings, and Related Topics, Conference in Honor of Ernest Shult
March 22-24, 2001
Kansas State University
Manhattan, KS, USA

Organizers
Michael Aschbacher, Andrew Chermak, Zongzhu Lin, Bernd Stellmacher

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Groups of even and p-type
by
Inna Korchagina
The OSU
Coauthors: Prof. R. Solomon

Extending the work of Thompson, Klinger and Mason in 1975 initiated the study of the groups of characteristic {2, p}-type. More recently Gorenstein and Lyons weakened the notion of characteristic 2-type to even type. In this more general context we prove the following theorem of Klinger-Mason type:

Theorem Let G be a finite simple K-group of even type which satisfies the following conditions:

e(G)=3;

If p is an odd prime such that m_{2, p}(G)=3 and B =~ E₂₇ is contained in a 2-local subgroup of G, then for every nontrivial subgroup A of B, F^*(C_G(A)) = O_p(C_G(A)).

Then G =~ Co₃.

Date received: March 7, 2001