Induced maps in homology for p-toral compact Lie groups

For stable splittings of the classifying spaces of general p-toral compact Lie groups, it is important step to describe the induced maps of the stable maps on Fp-homology. In this paper, we give the structure of the induced maps on Fp-homology for the classifying spaces of p-toral compact Lie groups. For this purpose, we show that there exists a transfer map τ : BF∞p∧ → BH∞p∧ where F∞ is a p-discrete toral group and H∞ is a subgroup of F∞ and we combine this result with the property that Af(F∞, K) is dense in lim←nA(Fn, K)p∧.