📝 SummarXiv

Abstract

Let $F$ be a field of prime order $p$ and let $\bar{F}$ denote an algebraic closure of $F$. Then for any finite group $G$ we obtain a well-defined surjective map $\Gamma$ from the set of finitely generated isomorphism types of indecomposable $\bar{F}G$-modules, $(\text{ITI}(\bar{F}G))$ to the corresponding set of $FG$-modules $(\text{ITI}(FG))$ such that if $X$ is a finitely generated indecomposable $\bar{F}G$-module, then $X$ and $\Gamma(X)$ share some important common Green Theory Invariants. We also prove a similar result for simple modules and a formula for the number of isomorphism types of simple $\bar{F}G$-modules.