Research output: Contribution to Journal/Magazine › Journal article
Research output: Contribution to Journal/Magazine › Journal article
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TY - JOUR
T1 - Glauberman and Thompson's theorems for fusion systems.
AU - Diaz, Antonio
AU - Glesser, Adam
AU - Mazza, Nadia
AU - Park, Sejong
N1 - First published in Proceedings of the American Mathematical Society in 137, 2009, published by the American Mathematical Society. Copyright 2008, American Mathematical Society
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
U2 - 10.1090/S0002-9939-08-09690-1
DO - 10.1090/S0002-9939-08-09690-1
M3 - Journal article
VL - 137
SP - 495
EP - 509
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 1088-6826
ER -