Basic abstract algebra, pt.14

This is a video series about basic abstract algebra and group theory. We will keep it basic so that anyone can follow the videos.

This is the fourteenth video in the series. We start to look at factor groups and cosets.

Category:

Education

Tags:

• basic
• abstract
• algebra
• group
• number
• theory
• mathematics
• Abel
• math
• theorem
• prove
• proof
• science
• axioms
• subgroup
• abel
• abelian
• division
• algorithm
• modulo
• divisible
• coset
• factor
• groups
• Gauss

[colverjustin]

im hoping when you said the same remainder when dividing by n!, that the ! is purely an exclamation

[VeritySeeker]

@colverjustin I hope so too ;). Yes, you're right.

[interted]

i'm having trouble understand the notation you use for defining sets: ex. gH={gh|hЄH}. First I thought that | meant divides, but now I see that it is equal to : as it appears in my book, which means "as this statement stands". Am I right?

[VeritySeeker]

Hi, yes you are right. A way to read it is like this:

{gh | h in H}

All of the form gh such that h is in H.

I read | as "such that".

So it would be every element that is equal to gh for some h in H. Or... all gh, as h runs through H. Many ways to think of it, and pick the one you prefer.

Yes you are right it is the same as : in your book. Some use that notation aswell.

[humby123]

Brilliant. Don't stop making these or we will just have to go back to seeing monkeys drink their own urine.

[TheBlackwaterDemon]

Looking forward to more!

[Emperorlawson]

I've found in my undergraduate math studies that a small dry erase board w/ some markers is an invaluable study tool. Beats burning a hole in paper with an eraser lol.

[ironclownfish]

Great videos!! I was confused at first though when you were defining cosets. The vertical "such that" line looks like the line you used for "divides". As in 4|8

[Ezzyman17]

Around 2:55 you say that "It is possible that to prove that..... H in G" and then suddenly it changes to G in H? Maybe just a mistake or i don't understand it?

[jimmydu444]

mind = blown

[1991DANYLO2010]

ALL IN EVERYWHERE WAS LISTENIG THIS VIDEO ALSO I UNDERSTOOD IT(DANYLO)-THE SMALL GOD

[1gombro]

indeed! that's great. one of the most enjoyable and comprehensible videos on the server. At the vert beginning the music seemed a bit disturbing but now I cannot image any other music played here:)

[MinGophers]

more more more! I love em!