Glauberman's and Thompson's theorems for fusion systems

Authors:
Antonio Díaz, Adam Glesser, Nadia Mazza and Sejong Park

Journal:
Proc. Amer. Math. Soc. **137** (2009), 495-503

MSC (2000):
Primary 20C20

DOI:
https://doi.org/10.1090/S0002-9939-08-09690-1

Published electronically:
September 17, 2008

MathSciNet review:
2448569

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove analogues of results of Glauberman and Thompson for fusion systems. Namely, given a (saturated) fusion system on a finite -group , and in the cases where is odd or is -free, we show that (Glauberman) and that if , then (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.

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Additional Information

**Antonio Díaz**

Affiliation:
Department of Mathematical Sciences, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

Address at time of publication:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

Email:
adiaz@math.ku.dk

**Adam Glesser**

Affiliation:
Department of Mathematical Sciences, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

Address at time of publication:
Mathematics and Computer Science Department, Suffolk University, Fenton Building, Room 621, 32 Derne Street, Boston, Massachusetts 02114

Email:
aglesser@suffolk.edu

**Nadia Mazza**

Affiliation:
Department of Mathematical Sciences, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

Address at time of publication:
Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4FY, United Kingdom

**Sejong Park**

Affiliation:
Department of Mathematical Sciences, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

Email:
s.park@maths.abdn.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-08-09690-1

Received by editor(s):
February 7, 2008

Published electronically:
September 17, 2008

Additional Notes:
The first author was supported by EPSRC grant EP/D506484/1 and partially supported by MEC grant MTM2007-60016.

The third author’s research was supported by Swiss National Research Fellowship PA002-113164/1.

Communicated by:
Jonathan I. Hall

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.