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Basic Abstract Algebra by S. K. Jain, S. R. Nagpaul, P. B. Bhattacharya

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CHAPTER 5

Normal subgroups

1 Normal subgroups and quotient groups

We recall that multiplication in a group G induces a product of any two subsets A and B of G, given by images. 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 images, if images for every

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