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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) –  Tobias Kildetoft Jul 10 '12 at 10:46
    
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. –  Aaron Jul 10 '12 at 15:07

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