Control of transfer and weak closure in fusion systems.

Diaz, Antonio and Glesser, Adam and Mazza, Nadia and Park, Sejong (2010) Control of transfer and weak closure in fusion systems. Journal of Algebra, 323 (2). pp. 382-392. ISSN 0021-8693

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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.