On symmetric quotients of symmetric algebras

We investigate symmetric quotient algebras of symmetric algebras, with an emphasis on finite group algebras over a complete discrete valuation ring OO. Using elementary methods, we show that if an ordinary irreducible character χ of a finite group G   gives rise to a symmetric quotient over OO which is not a matrix algebra, then the decomposition numbers of the row labelled by χ are all divisible by the characteristic p   of the residue field of OO.