8

Maschke’s Theorem

We now come to our first major result in representation theory, namely Maschke’s Theorem. A consequence of this theorem is that every *FG*-module is a direct sum of irreducible *FG*-submodules, where as usual *F* = or . (The assumption on *F* is important – see Example 8.2(2) below.) This essentially reduces representation theory to the study of irreducible *FG*-modules.

**Maschke’s Theorem**

*8.1 Maschke’s Theorem*

*Let G be a finite group, let F be* *or* , *and let V be an FG-module. If U is an FG-submodule of V, then there is an FG-submodule ...*

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