# 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)
• Published : 1997.02.01

#### Abstract

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.

#### References

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