Definition of Normal Subgroup and one example - Chapter 6 - Lecture 1

We begin this chapter by defining a normal subgroup. In the sequel we will be looking at several equivalent definitions of a normal subgroup, however we begin with the one where a subgroup is said to be normal iff every left coset is equal to the corresponding right coset. We also remark that the trivial and the improper subgroups of a group will always be normal. We illustrate that A_3 is a normal subgroup of S_3 by evaluating and comparing all left and right cosets of A_3.

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