COMPLEX BORDISM OF CLASSIFYING SPACES OF THE DIHEDRAL GROUP

In this paper, we study the $BP_*$-module structure of $BP_*$(BG) mod $(p,v_1,{\cdots})^2$ for non abelian groups of the order $p^3$. We know $grBP_*(BG)=BP_*{\otimes}H(H_*(BG);Q_1){\oplus}BP^*/(p,v_1){\otimes}ImQ_1$. The similar fact occurs for $BP_*$-homology $grBP_*(BG)=BP_*s^{-1}H(H_*(BG);Q_1){\oplus}BP_*/(p,v)s^{-1}H^{odd}(BG)$ by using the spectral sequence $E^{*,*}_2=Ext_{BP^*}(BP_*(BG),BP^*){\Rightarrow}BP^*(BG)$.