| Institution: | Department of Mathematical Sciences, University of Aberdeen, Meston Building, Abderdeen, AB24 3UE United Kingdom Markus Linckelmann ; Department of Mathematical Sciences, University of Aberdeen, Meston Building, Abderdeen, AB24 3UE United Kingdom |
| Abstract: | For  an odd prime, we generalise the Glauberman-Thompson  -nilpotency theorem (Gorenstein, 1980) to arbitrary fusion systems. We define a notion of  -free fusion systems and show that if  is a  -free fusion system on some finite  -group  , then  is controlled by  for any Glauberman functor  , generalising Glauberman's  -theorem (Glauberman, 1968) to arbitrary fusion systems. |
-theorems for fusion systems