How to Define Homomorphisms on Quotient Groups

One way to define a function on a quotient group is to define it in terms of the coset representatives. However, this approach runs into problems of well-definedness. This video explains how we can address that problem.
0:00 Problem Introduction
5:42 Solution
10:34 Non-example: Integers mod 5
11:13 Example: Alternating Group
Group Theory playlist: • Group Theory
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Music: C418 - Pr Department

[@user-wl9dv2gx3p]

Love your videos. All are well done and clearly presented. Wish you are well; as I saw that the last video was a year ago.

[@zakbettman8376]

Upload more bro ur very talented at teaching this with confidence at such a young age

[@pledab]

OMG I was learning about this in my homoquotient class.

[@strikeemblem2886]

P.S. in advanced texts, this is referred to as "The map phi:G->H factors through the quotient G/K"

[@kungfumartialarts]

Can you do a grass roots introduction to a college math topic? While I know there are others out there doing them, it would be nice to see your explanations on the basics. Sometimes we like a particular teacher, but either the problems presume too much knowledge or the courses are not available. I appreciate your channel., but it would be nice to see something like Real Analysis from scratch. Cheers.

[@jo5i4h]

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[@andrewgraybar4984]

1,700,000 views. Umm, NIL; can we suggest one dollar per view ? Just wondering.

[@BuddyNovinski]

No, our distinguished young man doesn't want money. He's putting out, and should eventually be so rewarded. I am reminded of a professor when I was taking calculus (around the bicentennial) who told me that she was taking abstract algebra, but the problem was one of the three that I've learned from math much later: she wasn't anywhere as clear as these videos. The other two are to learn the concepts and to practice the problems. Of course, there's the adage: Why must we grow old to become smart?😀