= Integral form of a group representation
{title2=$W\subset V$}
For a <p-modular system> $(K,\mathcal O,k)$, an integral form of a finite-dimensional $KG$-<module> $V$ is a $G$-stable finite free $\mathcal O$-submodule $W\subset V$ with $K\otimes_{\mathcal O}W\cong V$. Starting with a basis lattice $L$, the sum $\sum_{g\in G}gL$ supplies such a form: it is finitely generated and <torsion-free>, hence free over the <discrete valuation ring> $\mathcal O$. Reduction gives the $kG$-module $W/\pi W$, where $\pi$ is a <uniformizer>.
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