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Feb 5, 2010 at 4:21 comment added Jack Schmidt J.L. Alperin's "Sylow Intersections and Fusion" (MR0215913; DOI: 10.1016/0021-8693(67)90005-1) is a nice group theoretic introduction to some of the key ideas behind fusion. It is a more precise version of Sylow's conjugacy theorem. Linckelmann's introduction (MR2336638) is one of the easiest ways to read the category theoretic version of fusion. Alperin's Local Representation Theory textbook introduces the Brauer subpairs theory nicely; that is the other main source of fusion systems.
Nov 16, 2009 at 16:09 comment added Harrison Brown Yeah, okay, good point; it's probably too much to hope for there to be something easy enough to apply in day-to-day situations. But there's no obvious reason (to me, anyway) that there shouldn't be an extension even to finite groupoids.
Nov 16, 2009 at 6:16 comment added Charles Siegel I learned the Sylow theorems precisely like that. Homework problem in my abstract algebra class "Show that there are no nonabelian simple groups of order less than 60."
Nov 16, 2009 at 5:08 history answered S. Carnahan CC BY-SA 2.5