Diaz, Antonio and Glesser, Adam and Mazza, Nadia and Park, Sejong (2009) Glauberman and Thompson's theorems for fusion systems. Proceedings of the American Mathematical Society, 137. pp. 495-509.
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Official URL: http://dx.doi.org/10.1090/S0002-9939-08-09690-1
Abstract
We prove analogues of results of Glauberman and Thompson for fusion systems. Namely, given a (saturated) fusion system $\CF$ on a finite $p$-group $S$, and in the cases where $p$ is odd or $\CF$ is $S_4$-free, we show that $\Z(\N_\CF(\J(S)))=\Z(\CF)$ (Glauberman), and that if $\C_\CF(\Z(S))=\N_\CF(\J(S))=\CF_S(S)$, then $\CF=\CF_S(S)$ (Thompson). As a corollary, we obtain a stronger form of Frobenius' theorem for fusion systems, applicable under the above assumptions, and generalizing another result of Thompson.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Proceedings of the American Mathematical Society |
| Additional Information: | First published in Proceedings of the American Mathematical Society in 137, 2009, published by the American Mathematical Society. Copyright 2008, American Mathematical Society |
| Subjects: | Q Science > QA Mathematics |
| Departments: | Faculty of Science and Technology > Mathematics and Statistics |
| ID Code: | 20813 |
| Deposited By: | Dr Nadia Mazza |
| Deposited On: | 03 Dec 2008 11:07 |
| Refereed?: | No |
| Published?: | Published |
| Last Modified: | 26 Jul 2012 15:40 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/20813 |
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