Extensions of Group Representations Over Fields of Prime Characteristic

Burton Fein
1969 Proceedings of the American Mathematical Society  
pal indecomposable K[H]-module such that Ulq)=U for all gEG. Let M be the unique minimal submodule of U. Clearly M(a)=M for all gEG so by Lemma 3, M is extendible to a A[c7]-module N, Na = M. Let V be a principal indecomposable A^[G]-module having A as its unique minimal submodule. In view of Theorem (2B) of [4], to prove that Vh = U it is sufficient to show that U\ Vr-. Let R be the sum of the irreducible X[il]-submodules of F#. Then M = NH ER so M is a direct summand of R. But Vh is injective
more » ... and so contains an injective hull of M [l, Theorem 57.13]. Since U is the injective hull of M we have proved that U is extendible to V.
doi:10.2307/2037476 fatcat:wrvah7nq3vco3b5baxlzwtqqyu