Properties of Homomorphisms - Chapter 8 - Lecture 5

Here we begin with a homomorphism from one group G into another group G'. We then prove the following properties: (1) Identity e in G is mapped to identity e' in G' (2) image of the inverse of an element is the inverse of the image of that element (3) image of a^n is (image of a)^n, for all integers n (4) order of image of an element divides the order of the element.
Errata in writing on board @ 10mins 13 secs: I have written m belongs to Z whereas I have said and intended to write m belongs to N i.e. the set of natural numbers.

Link to the previous lecture

Link to the next lecture

Link to the first lecture of this chapter