Abstract
In this note, we briefly introduce the theory of fusion systems and some recent progress. Fusion systems were introduced by Puig in the early 1990s as a common framework for fusion systems of finite groups or $p$-blocks of finite groups. Fusion systems are also very important in algebraic topology, the long-open conjecture by Martino and Priddy is thus solved. In recent two decades the theory develops very quickly with deep applications. A simplified proof of the classification theorem of finite simple groups is highly expected.
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