A Characterization of Permutation Modules Extending a Theorem of Weiss

摘要

Let (G) be a finite (p)-group with normal subgroup (N). A celebrated theorem of A. Weiss gives a sufficient condition for a (mathbb{Z}_pG)-lattice to be a permutation module, looking only at its restriction to (N) and its (N)-fixed points. In case (N) has order (p), we extend the condition of Weiss to a characterization.