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Maschke's Theorem does generalise to arbitrary (commutative) coefficient rings. If $|G|$ is a unit in $R$, then every $R[G]$-module is a direct summand of a module induced from the trivial subgroup. …

It is generally not rigid at all. Note that if $U$ lifts an absolutely irreducible $kG$ module, then $\overline{U}$ is certainly uniquely defined upto isomorphism (though absolutely irreducible $kG$- …

Let O be a complete discrete valuation ring and G a finite group. Recall that a finitely generated O-free OG-module $M$ such that the traces of the invertible endomorphisms of $M$ generate a strictly …

My character theory is rather weak, so excuse me if this is a triviality. I have read on the encyclopedia of maths that for any group $G$, every block of $G$ contains an irreducible character of hei …

Given a (splitting) $p$-modular system $(K, \mathcal{O}, k)$ for a finite group $G$, any given simple character $\chi$ is afforded by some $KG$ module $V_\chi$, and there in general many non-isomorphi …