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A reduction theorem for fusion systems of blocks

Kessar, R. & Stancu, R. (2008). A reduction theorem for fusion systems of blocks. Journal of Algebra, 319(2), pp. 806-823. doi: 10.1016/j.jalgebra.2006.05.039


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 p-local finite groups over the extra-special group of order p3 and exponent p, Math. Z. 248 (2004) 45–65] do not occur as fusion systems of p-blocks of finite groups.

Publication Type: Article
Publisher Keywords: blocks, fusion systems, extra-special groups
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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