Block for a group

Definition with symbols
Let $$G$$ be a group and $$k$$ a field. A block of $$G$$ over $$k$$ is a block of this algebra. Here,a a block of an algebra means one of the members of a maximal decomposition of the algebra as a direct sum of algebras.

In the case when the characteristic of $$k$$ does not divide the order of $$G$$, the blocks are simply the matrix rings corresponding to the irreducible representations of $$G$$.

The theory of blocks becomes interesting in the case when the characteristic of $$k$$ divides the order of $$G$$.