We recall that multiplication in a group *G *induces a *product* of any two subsets *A* and *B* of *G,* given by . If *A* or *B* is a singleton, we write *aB* for {*a*}*B* and *Ab for* *A*{*b*}. Since multiplication in *G* is associative, the induced multiplication of subsets of *G* is also associative.

**Definition.** *Let G be a group. A subgroup N of G is called a* normal *subgroup of G, written* *, if* * for every*

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