Abstract
We give a result on Cartan invariants of the group algebra k G kG of a finite group G G over an algebraically closed field k k , which implies that if the Loewy length (socle length) of the projective indecomposable k G kG -module corresponding to the trivial k G kG -module is four, then k k has characteristic 2. The proof is independent of the classification of finite simple groups.
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