The Image of a Group Homomorphism is a Subgroup (Proof)

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We are given a group homomorphism from a group G into a group H. We prove that the image of f, the collection of all elements of the form f(x) where x is in G, is a subgroup of H. I hope this helps someone learning abstract algebra.

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I don't know much about this. I can only wonder what I was wondering about Real Analysis: Why do you need G or H or anything else to be closed? If G = R, then it's not closed. If it's not R, where are the end brackets? OR, is this just a general case proof and the details will be supplied in the specific problems where this aspect of math is used?

SequinBrain

You may occasionally hear "x dash" instead of "x prime".
(:

ardiris

Tomorrow is my maths exam . A lovely comment from you will make it obvious to score good grades professor.

shivanijugran

Amazing explanations! Also, do you have other alegbra lessons in a playlist?

cartoonzer

I get very excited when ur videos get uploaded 🤩

electragex

The Image of a Group Homomorphism is a Subgroup (Proof)

The Image of a Group Homomorphism is a Subgroup (Proof)

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