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## Control of transfer and weak closure in fusion systems.

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Journal publication date 15/01/2010 Journal of Algebra 2 323 11 382-392 Published 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.