Existence of subpolynomial algebras in $H^*(BG,Z/p)$

  • Lee, Hyang-Sook (Department of Mathematics, Ewha Women's University, Seoul 120-750) ;
  • Shin, Dong-Sun (Department of Mathematics, Ewha Women's University, Seoul 120-750)
  • 발행 : 1997.02.01


Let G be a finiteg oroup. We denote BG a classifying space of G, which a contractible universal principal G bundle EG. The stable type of BG does not determine G up to isomorphism. A simple example [due to N. Minami]is given by $Q_{4p} \times Z/2$ and $D_{2p} \times Z/4$ where ps is an odd prime, $Q_{4p} is the generalized quarternion group of order 4p and $D_{2p}$ is the dihedral group of order 2p. However the paper [6] gives us a necessary and sufficient condition for $BG_1$ and $BG_2$ to be stably equivalent localized et pp. The local stable type of BG depends on the conjegacy classes of homomorphisms from the p-groups Q into G. This classification theorem simplifies if G has a normal sylow p-subgroup. Then the stable homotopy type depends on the Weyl group of the sylow p-subgroup.


  1. Annals of Math. Corrections Annals of Math v.111 Finite H-spaces and algebra over the steenrod algebra J. F. Adams;C. Wilkerson
  2. Method of Representation Theory with Applications to Finite Groups and Orders, Vol1 - Pure and Applied Mathmatics v.1 C. W. Curtis;I. Reiner
  3. The Cohomology of Groups L. Evens
  4. p-adic Numbers, p-adic Analysis and Zeta Functions N. Koblitz
  5. Canadian Mathematical Bulletin The stable and unstable types of classifying spaces Hyang-Sook Lee
  6. Bulletin of the American Mathematical Society v.27 A classification of the stable type of BG J. Martino;S. Priddy