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A classification of the stable type of $ BG$

Authors: John Martino and Stewart Priddy
Journal: Bull. Amer. Math. Soc. 27 (1992), 165-170
MSC (2000): Primary 55R35; Secondary 20F38, 55P15, 55P42
MathSciNet review: 1145578
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Abstract: We give a classification of the p-local stable homotopy type of BG, where G is a finite group, in purely algebraic terms. BG is determined by conjugacy classes of homomorphisms from p-groups into G. This classification greatly simplifies if G has a normal Sylow p-subgroup; the stable homotopy types then depends only on the Weyl group of the Sylow p-subgroup. If G is cyclic $ {\bmod \;p}$ then BG determines G up to isomorphism. The last class of groups is important because in an appropriate Grothendieck group BG can be written as a unique linear combination of BH's, where H is cyclic $ {\bmod \;p}$.

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Article copyright: © Copyright 1992 American Mathematical Society

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