All About Subgroups | Abstract Algebra

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

Abstract Algebra Exercises:

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[WrathofMath]

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[DrMathKinzie]

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 "<").

[linonator]

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[hamzaker]

What a great channel ! THIS IS UNDERRATED

[Bedoroski]

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 ;)

[enderesting]

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

[drapwill]

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

[nazombie]

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

[nilanjanabose]

You made this chapter very clear thank you❤ from india

[MrCoreyTexas]

I was watching another mathematician and he has H<=G for the subgroup concept, which looks like less than or equal to, I like your notation better, it looks like a little 45 degree angle which distinguishes it from <=.

[xylynpasol]

Thank you so much! Very clear explanation.

[laurenfung]

this video saved me from my math test !

[JesyrelAndrew]

Really cool. Well explained. I enjoyed though

[ronbitan]

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?

[l.JAI.SHREE.RAM.l]

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🙏

[Channel-zbfi]

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?

[SkinnyMMA]

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

[dripici]

we fa pt facultate ca am nevoie poimaine la fai

[jarrenblake]

Fun fact you lost 30% battery life during this vid