20

Restriction to a subgroup

In this chapter and the next, we are going to look at ways of relating the representations of a group to the representations of its subgroups. Here, we introduce the elementary idea of restricting a *G*-module to a subgroup *H* of *G*, and illustrate its use. The case where *H* is a normal subgroup of *G* is of particular interest, and Clifford’s Theorem 20.8 gives important information in this case. We apply this result in the situation where *H* is of index 2 in *G*, which occurs, for example, when *G* = *S _{n}* and

**Restriction**

Let *H* be a subgroup of the finite group *G*. Then *H* is a subset of *G*. If *V* is a *G*-module, then *V* is also ...

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