A note on stable Clifford extensions of modules

Abstract

Let $H$ be a normal subgroup of $G$. Let $W$ be a $G$-invariant indecomposable $\mathit{RH}$-module with vertex $Q$. Let $V$ be an indecomposable direct summand of the induced module $W^{G}$. Let $W'$ and $V'$ be the Green correspondents of $W$ and $V$ in $N_{H}(Q)$ and $N_{G}(Q)$ respectively. Then we prove that $\rank_{R} V/{\rank_{R}} W=\rank_{R} V'/{\rank_{R}} W'$.