2
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if I found indecomposable $K[G]$ modules, are there any techniques to get from this irreducible $K[G]$ modules?

(e.j. for $k=\mathbb{Z}/p \mathbb{Z}$ and $G=C_p$)

regards, Khanna

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    The specific case you mention is easy, since any irreducible representation of a finite $p$-group over a field of characteristic $p$ is trivial (see for example Gorenstein's Finite Groups)2012-07-10
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    I think what you want to do translates into "finding decomposition matrix of $KG$, and this is in general very hard for $\mathrm{char} K$ divides $|G|$, otherwise, the $KG$ is semisimple, so indecomposable and irreducible is the same.2012-07-10

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