All About Subgroups | Abstract Algebra

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We introduce subgroups, the definition of subgroup, examples and non-examples of subgroups, and we prove that subgroups are groups. We also do an example proving a subset is a subgroup. If G is a group and H is a nonempty subset of G, we say H is a subgroup of G if H is closed with respect to inverses and closed under the group operation of G. #abstractalgebra #grouptheory
What are Groups?: • What is a Group? | Abs...
Abstract Algebra Course: • Abstract Algebra
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Опубликовано:

2 окт 2024

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Комментарии : 49

@WrathofMath Месяц назад

Support the production of this course by joining as a Channel Member to get exclusive videos, original music, lecture notes, and more: ru-vid.com/show-UCyEKvaxi8mt9FMc62MHcliwjoin Abstract Algebra Course: ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN Abstract Algebra Exercises: ru-vid.com/group/PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz

@DrMathKinzie Год назад

The asterisks usually are used to denote the non-zero rationals/reals/complexes, rather than the positive ones. In particular, there is no possible notion of "positive" for the complex numbers (no linear ordering that satisfies the usual properties of "

@MrCoreyTexas 2 месяца назад

The first thing I thought of when I saw positive complex numbers was wait what does that mean? The real part is positive, the imaginary part is positive, both are positive?

@linonator Год назад

Hey man! Just want to give a huge thanks to you. I just found your channel and from one video you helped unlock my understanding of something I was having trouble with. Thank you for create content like this. You really are making an impact on complete strangers for the better. Thanks again and keep up the great content

@WrathofMath Год назад

Thanks so much! Llet me know if you have any requests!

@o_oyxy 8 месяцев назад

i love you bro youre carrying me

@hamzaker829 Год назад

What a great channel ! THIS IS SOOOOO UNDERRATED

@l.JAI.SHREE.RAM.l 3 месяца назад

Sir, I have a doubt, at many places group is represented by G how can it be possible, G may be a set not group, group should always denoted by (G,*). Please clear it🙏

@MrCoreyTexas 2 месяца назад

I was watching another mathematician and he has H

@Bedoroski Месяц назад

Your presentation is even better than actual textbooks! I'm looking forward to more of these content, and maybe a future textbook of your own ;)

@WrathofMath Месяц назад

Thanks so much! There are many more videos on the way - right now my focus is finishing linear algebra, but I'll come back to the abstract algebra series shortly. I did just recently add a couple of new videos. I'm particularly excited to make more alg videos with my improved penmanship!

@ronbitan2641 Год назад

Hello! According to the rule you gave where H has to be closed with respect to inverses and multiplication, ehy multiplication? What if the operation of the group is + for example? Does it still need to be closed under multiplication or does it depend on the operation?

@WrathofMath Год назад

As long as we're talking about groups, "multiplication" is just short for "the operation". We generally default to multiplicative notation and verbiage unless we know we're dealing with an additive group. Does that make sense? Definitely check out my abstract algebra playlist and the exercises playlist for more, here's a link to an unreleased video on subgroup tests you may find as useful follow up: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-poQXf90tcFM.html

@enderesting Год назад

This video is the best explanation for subgroups on youtube :,)) Thank you so much! I found a lot of videos confusing because they never explain the definition of subgroup or give any example. This is perfect :,3

@WrathofMath Год назад

Thank you - so glad it helped! I am trying to make my Abstract Algebra playlist the best around! Will be working hard on it this summer. ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN

@punditgi Год назад

More good stuff. Nice! 😃

@WrathofMath Год назад

Thank you! In a real abstract alg mood lately!

@JesyrelAndrew 6 месяцев назад

Really cool. Well explained. I enjoyed though

@WrathofMath 6 месяцев назад

Awesome, thank you!

@allstar965 Год назад

Thanks a lot! Very informative!

@WrathofMath Год назад

Thanks for watching! Isomorphic group lesson comes out tonight - lots more algebra to come!

@nazombie7935 6 месяцев назад

Thank you sire!! This video helped my understanding of subgroups so much

@nilanjanabose3059 Год назад

You made this chapter very clear thank you❤ from india

@tirtahadith 2 месяца назад

Done

@AlfredoPadin-f8j 6 месяцев назад

What note taking app are you using?

@drapwill 10 месяцев назад

Absolutely love your channel thus far! Your explanations have unraveled some major knots in my mathematical thinking. Outstanding!

@WrathofMath 10 месяцев назад

Thanks so much!

@Channel-zb1fi 11 месяцев назад

When you test for if a set is closed under some operation, do you have to test for the element multiplied by itself or do the elements have to be distinct? If that is the case then how do you go about dealing with sets containing only one element?

@jonko82 11 месяцев назад

When you you want to prove closure under the operation you simply pick two arbitrary elements from the set. Those arbitrary elements may or may not be distinct. In the example in the video loga and logb might be two distinct elements or they might be the same element. The proof holds either way. When you want to disprove closure you just need to find any two elements of the set that, when combined, do not produce another element of the set. Those two elements may or may not be distinct also.

@xylynpasol9831 6 месяцев назад

Thank you so much! Very clear explanation.

@WrathofMath 6 месяцев назад

Glad it was helpful! Check out the playlist for more if you haven't already! ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN

@jarrenblake2886 Год назад

Fun fact you lost 30% battery life during this vid

@WrathofMath Год назад

That's more a depressing fact haha. Time for a new iPad!

@SkinnyMMA 10 месяцев назад

Why do we consider multiplicative inverse of a and NOT additive inverse in 13:59

@WrathofMath 10 месяцев назад

That's just log properties. We had -log a, and that is the same as log (a^-1). In general, xlog(y) = log(y^x). Does that answer your question?

@SkinnyMMA 10 месяцев назад

@@WrathofMath oh actually I get it now... Btw, I knew about this log property, now I don't understand why on earth I asked this query 😅... Thanks though for listening out

@dripici4371 Год назад

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@laurenfung7265 Год назад

this video saved me from my math test !

@WrathofMath Год назад

So glad it helped!

@guddu1958 Год назад

Don't you ever get tired 😴

@WrathofMath Год назад

Often!

@liketsontobo8463 Год назад

great video bro! keep it up

@WrathofMath Год назад

Thank you - I will, let me know if you ever have any questions!

@delzeltyna Год назад

thank you!!!❤

@WrathofMath Год назад

Glad to help! Check out my abstract algebra playlist if you're looking for more, and let me know if you have any questions!: ru-vid.com/group/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN

@raulbeienheimer Год назад

Thanks!

@WrathofMath Год назад

Glad to help - thanks so much for your support, Raül! Let me know if you ever have any questions, I will be making a lot more Abstract Algebra content this summer.