Abstract Algebra: The definition of a Subgroup

Learn the definition of a subgroup.

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

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[varsharoy]

the current generation needs to build teachers like you...well done

[light]

You makes abstract math more fun and easier to understand. What a talented teacher!

[Mrpallekuling]

Quite often these symbols are used instead: H⊆G and H⊂G. Thanks for good videos!

[rebekahadrian]

I'm just learning abstract algebra for fun, and these videos are great! Thanks so much Socratic! The lady is a great teacher!!!

[chetansharaf]

Wow...what a wonderful way of presenting the subject. Please make more videos related to maths

[pureroseangemuse]

I love how u made abstract algebra so easy… short videos and easy terms

[yusraiftikhar]

You are amazing!! Loads of live from pakistan. You made it so interesting .

[zairaner]

"Don't ever say that mathematicians aren't creative/predictable". Hey ofc they are creative. Just look how they named similar things: subsets, Subrings, subfields, submodules, subvectorspaces, .. xd

[abhinavkumar]

how to define that subgroup of a group

[RJ-rcdf]

Thank you for making the "ONE OF THE MOST DIFFICULT SUBJECT THAT I ENCOUNTERED" easy. <3 <3 .

[sanjursan]

You might emphasize a couple of points about subgroups:

1) the group operation of H is the same as that of G, where H < G.

2) the group identity of G must be the same as the group identity of H, so any subgroup of G will always contain e of G.

3) H itself is closed under the group operation.

4) since elements of H < G are also element of G, the inverses of elements of H are same a they are in G.

5) develop quotient groups by admitting: for any constant g in G and all h in H, the set of all gh, and the equivalence classes of subgroups that result.

[sonampriya]

You just changed my mind about abstract algebra. You made it fun and it encouraged me that I can learn it.
- Thank you❤

[yashtailor]

Mathematicians are never predictable!! Hell

[manishyadav]

This is manish yadav
B.sc 2nd year student
This video is mostly helpful, excellent for explain🙏✌️

[ullasrathod]

Whoever is behind these videos. They are just incredible. Loved the way things are dramatically explained.

[smileyakhila]

These videos are hilarious and intriguing. Thank you so much for posting them. I've been having a tough time with abstract algebra and this is very helpful.

[johnpaulcook]

Similar to one of the previous remarks, a subgroup is not just a subset of a group that is also a group.  For example, the positive reals form a group (with multiplication) and are a subset of the reals, another group (under addition).  But there is no subgroup relationship here.  A more precise definition would be something to the effect of:  "a subset that is also a group under the operation of G."

[twilightsparkle]

"if you're particularly particular"
HAHA I LOVE THAT! :D

[brbhati]

What a sense of humour this lady is with!!! OMG!! God bless you! You are much more than a mathematician!

[kunalgautam]

there is special place for people like you in HEAVEN of love from INDIA