Kessar, R. & Stancu, R. (2008). A reduction theorem for fusion systems of blocks. Journal of Algebra, 319(2), pp. 806823. doi: 10.1016/j.jalgebra.2006.05.039

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Abstract
Let k be an algebraically closed field of characteristic p and G a finite group. An interesting question for fusion systems is whether they can be obtained from the local structure of a block of the group algebra kG. In this paper we develop some methods to reduce this question to the case when G is a central p′extension of a simple group. As an application of our result, we obtain that the ‘exotic’ examples of fusion systems discovered by Ruiz and Viruel [A. Ruiz, A. Viruel, The classification of plocal finite groups over the extraspecial group of order p3 and exponent p, Math. Z. 248 (2004) 45–65] do not occur as fusion systems of pblocks of finite groups.
Item Type:  Article 

Uncontrolled Keywords:  blocks, fusion systems, extraspecial groups 
Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/1894 
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