Abstract
We study phantom maps in the stable module categoryStMod(kG), wherekis a field andGis a finite group. In this article we almost exclusively deal with maps out of countably generated modules. We show that the spacePhkG(M,N) of stabilized phantom mapsM→Nhas an expression as alim1←space which allows some control on its vanishing. Then we present a situation where all maps are phantom and need not be trivial. We provide explicit details for such a particular situation. Finally we construct a universal phantom map. We use it to show that the composite of two phantom maps is trivial and to characterize the modules with no nontrivial outbound phantom maps.
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