Algebra and Topology Seminar

4pm Tuesday 26 November 2002

Gemma Parmeggiani
University of Padova

The P!-Theorem and the P^~!-Theorem

The P!-Theorem (joint work with Ch.W. Parker and B. Stellmacher, to appear in J.Algebra) and the P^~!-Theorem (joint work with M. Mainardis, U. Meierfrankenfeld and B. Stellmacher, preprint) describe the structure and the embedding of certain p-minimal subgroups in finite K_p-groups of local characteristic p. This is a part of a project, initiated by U. Meierfrankenfeld, whose goals are to understand the structure of finite K_p-groups of local characteristic p and to classify them if p=2.

Here a group is a K_p-group of local characteristic p if its p-local subgroups U satisfy:

1. C_U(O_p(U)) < O_p(U), and
2. the simple sections of U are "known" simple groups.

The generic examples of groups of local characteristic p are the groups of Lie type defined over fields of characteristic p.

The classification of K₂-groups of local characteristic 2 would give an alternative proof of a major part of the classification of the finite simple groups.




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