For an arbitrary field F of
characteristic p ≧ 0, the usual partitioning of the p-regular elements of a finite group
G into F-classes (F-conjugacy classes) is extended to all of G in such a way that the
F-classes form a basis of a subalgebra Y of the class algebra Z of G over F. The
primitive idempotents of E ⊗FY , where E is an algebraic closure of F, are the same
as those of Z. By means of this fact it is shown that if p > 0 the number of blocks of
G over F with a given defect group D is not greater than the number of p-regular
F-classes L of G with defect group D such that the F-class sum of L in
Z is not nilpotent; equality holds if Op,p′,p(G) = G or if D is Sylow in G.
The results are generalized to arbitrary twisted group algebras of G over
F.
