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Control of transfer and weak closure in fusion systems.

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<mark>Journal publication date</mark>15/01/2010
<mark>Journal</mark>Journal of Algebra
Issue number2
Volume323
Number of pages11
Pages (from-to)382-392
<mark>State</mark>Published
<mark>Original language</mark>English

Abstract

We show that $\K_\infty$ and $\K^\infty$ control transfer in every fusion system on a finite $p$-group when $p \geq 5$, and that they control weak closure of elements in every fusion system on a finite $p$-group when $p \geq 3$. This generalizes results of G. Glauberman concerning finite groups.