Normal series and character values in p-standard table algebras

Abstract

ABSTRACTWe investigate the character values and structures of p-standard table algebras (A,B) with o(B) = pN. If N≤3, then B has a complete normal series. If for every χ∈Irr(B), χ has at most p distinct classes of character values, and if either B has a complete normal series or p = 2, then B is an elementary abelian p-group.