On the second lowey term of projectives of a group algebra
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LetG be a finite group andK a field of prime characteristicsp. LetA be an irreducibleKG-module andP G(A) the projective cover ofA. In this paper we show that
, where, for a groupH, Φp(H)=Φ(H modO p′(H)).
$$\Phi _p (C_G (A)) \leqq C_G (P_G (A)/P_G (A)J(KG)^2 ) \leqq C_G (A) \cap \Phi _p (G)$$
KeywordsExact Sequence Normal Subgroup Finite Group Irreducible Component Short Exact Sequence
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