Fusion Systems in Algebra and Topology
نویسندگان
چکیده
Let G be a finite group, p a prime, and S a Sylow p-subgroup of G. Subsets of S are said to be fused in G if they are conjugate under some element of G. The term “fusion” seems to have been introduced by Brauer in the fifties, but the general notion has been of interest for over a century. For example in his text The Theory of Groups of Finite Order [Bu] (first published in 1897), Burnside proved that if S is abelian then the normalizer in G of S controls fusion in S. (A subgroup H of G is said to control fusion in S if any pair of tuples of elements of S which are conjugate in G are also conjugate under H.)
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