Definition of Normal Subgroups | Abstract Algebra

We introduce normal subgroups with their conjugate definition and the coset definition. We'll see examples of normal subgroups and nonexamples of normal subgroups, and we finish with a proof that every subgroup of an abelian group is a normal subgroup. A subgroup H of a group G is normal if H is closed with respect to conjugates, or equivalently if each left coset aH is equal to each right coset Ha for every a in G. #abstractalgebra #grouptheory
Proving Equivalent Definitions of Normal Subgroups: • Equivalent Definitions...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises: • Abstract Algebra Exerc...
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[@golden_smaug]

It was so easy to understand normal subgroups with this video, unlike my previous 2 months in college lol. Thank you! :)

[@WrathofMath]

Glad it was helpful!

[@liketsontobo8463]

never disappoints, your videos are always clear, thank you so much

[@WrathofMath]

That's always what I'm going for! Thank you for watching!

[@MuniraDanish-w9x]

It was very helpful if you make a video about this topic with matrices and another complicated example of normal subgroup

[@MuniraDanish-w9x]

Thank you so much

[@jaubertnangola4205]

Very easy bro! I like your way to explain. Great tank for your help

[@WrathofMath]

Glad it helped! Thanks for watching!

[@PedroCristian]

6:38 the subgroup is the alternating group, being the kernel of the signature morphism, it is normal.

[@andersonrocha8186]

Maaaannnnn! Your explanations are great! Thank you so much!

[@WrathofMath]

Thank you! I really am trying to nail the clarity with my abstract algebra videos, glad to be helpful!

[@karinablanchard9511]

Thank u!

[@WrathofMath]

Glad to help - thanks for watching!

[@MrCoreyTexas]

Your notation at 5:00 is throwing me off. I'm used to seeing two rows enclosed with parenthesis for permutation groups like in a previous video in this series. Also why doesn't each of the x, and inv(x) have 3 elements, you just have "(2 3)" (I would expect (1 2 3) or something like that)

[@MrCoreyTexas]

I think I "decoded" your notation. If you look back to your video "Permutation Groups and Symmetric Groups", (2 3) corresponds to alpha = (1 2 3 / 1 3 2), and (1 2 3) must correspond to delta = (1 2 3 / 2 3 1). As I followed the order of the playlist, I never encountered this alternative notation. One of the challenges of teaching is putting yourself in the mind of a newbie :)

[@christopherrosson2400]

Fantastic stuff. Thank you

[@WrathofMath]

Glad to help - thanks for watching!

[@lukundonambela2374]

Your videos are so helpful 👏👏

[@WrathofMath]

So glad to help - thanks for watching and let me know if you ever have any questions!

[@VNFilmography]

Thank you!

[@WrathofMath]

You're welcome!

[@OgundipeSamuel-cp6xt]

Thank you soooooooo much 🤩

[@WrathofMath]

I’m glad to help!

[@vinuvs4996]

Very good lcture

[@WrathofMath]

Thank you!

[@MrCoreyTexas]

Is there a concept in mathematics called "concubine" lol that's what i think of when I hear "conjugate"

[@edauzun7879]

Thank you!!

[@WrathofMath]

Glad to help!