On certain algebras associated with finite groups

We construct new types of algebras which take into account the block structure of finite groups. We study the construction of such algebras. It is proved that the number of irreducible components of such an algebra is equal to the number of p blocks of the finite group whose defective groups contain a given p-element defined by the algebra. If the p-element is the unit, then the number of irreducible components is equal to the number of p-blocks of the finite group.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 901–911, July–August, 1991.