O'Reilly logo

Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 = image or image. (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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required