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

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4

FG-modules

We now introduce the concept of an FG-module, and show that there is a close connection between FG-modules and representations of G over F. Much of the material in the remainder of the book will be presented in terms of FG-modules, as there are several advantages to this approach to representation theory.

FG-modules

Let G be a group and let F be image or image.

Suppose that ρ: G → GL (n, F) is a representation of G. Write V = Fn, the vector space of all row vectors (λ1, . . . , λn) with λiF. For all vV and gG, the matrix product

of the ...

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