Daniel Palacín: The Fitting subgroup of a supersimple group

The logic seminar (HUJI)
takes place on Wednesdays at 16:00, in room 209
The speaker on March 19 is Daniel Palacín.

Title: The Fitting subgroup of a supersimple group.

Abstract: The Fitting subgroup of a given group G is the subgroup generated by all nilpotent normal subgroups of G. While it is always normal, it may not be nilpotent (neither definable). In fact, the nilpotency of the Fitting group implies its definability. In the model-theoretic paradise of stable groups, Wagner proved that the Fitting subgroup is always nilpotent, generalizing a result of Nesin in the finite Morley rank context. However, this is not known for the wider class of groups with a simple theory.

In this talk we present some of the main tools and notions of groups with a supersimple theory, and we prove that the Fitting subgroup of a supersimple group is nilpotent. This generalize a proof of Milliet in the finite rank context.

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