  One of the most beautiful results in the integral representation theory of
finite groups is a theorem of A. Weiss that detects a permutation $R$-lattice
for the finite $p$-group $G$ in terms of the restriction to a normal subgroup
$N$ and the $N$-fixed points of the lattice, where $R$ is a finite extension of
the $p$-adic integers. Using techniques from relative homological algebra, we
generalize Weiss' Theorem to the class of infinitely generated pseudocompact
lattices for a finite $p$-group, allowing $R$ to be any complete discrete
valuation ring in mixed characteristic. A related theorem of Cliff and Weiss is
also generalized to this class of modules. The existence of the permutation
cover of a pseudocompact module is proved as a special case of a more general
result. The permutation cover is explicitly described.
