Intro to Group Homomorphisms | Abstract Algebra
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- čas přidán 27. 07. 2024
- We introduce group homomorphisms with the definition, the definition of a homomorphic image, and several examples, including proof that certain functions are homomorphisms. We also show a non-example, a function from one group to another which is not a homomorphism. In short, a homomorphism f from a group G to a group H, is a function from G to H such that for all a, b in G, f(ab) = f(a)f(b). We say the homomorphism "preserves the group operation". #abstractalgebra #grouptheory
Group Isomorphisms: • Isomorphic Groups and ...
Basic Properties of Homomorphisms: • Proof: Basic Propertie...
Examples of Group Homomorphisms: coming soon
Kernels of Homomorphisms: • Kernels of Homomorphis...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises: • Abstract Algebra Exerc...
0:00 - What is a Homomorphism?
0:40 - Definition of a Homomorphism
2:59 - Definition of Homomorphic Image
4:30 - Example 1 (A homomorphism that is onto)
10:09 - Example 2 (A homomorphism that is not onto)
11:42 - Trivial Examples of Homomorphisms
12:25 - Non-Example (A function that is not a homomorphism)
13:03 - Two Basic Properties of Homomorphisms
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Socratica needs to watch out, your videos are way more clear than any I've seen
That’s a high compliment - thank you! Socratica really is the only competition I can see for well-produced abstract algebra videos, and they’re no longer active on that front. Michael Penn also occasionally makes some excellent algebra content.
The Greatest of all times!
Thank you so much for these!! Been using you to study for finals next week ...
Awesome, I'm glad to help! Good luck next week!
Thanks!
Nice explanation! 😊
Thanks Ezra!
Your vedios are really helpful and simple thankyou ❤️
Glad you like them!
Very understandbly explanation
Thank you!
Right on time for my finals!
Awesome! Good luck!
Very good!
Thank you!
Wonderful video
Thank you!
this subject is an absolute nightmare, thanks for making it slightly easier to understand!
what are you finding a nightmare?
@@cjjk9142 a bit of exaggeration 😅
I'm doing my best! Good luck and let me know if you ever have any questions!
2) f(a).f(inv(a)) = f(a.inv(a)) = f(e_g) = e_h
Hence f(inv(a)) is inverse of f(a)
Example @11.37, the H group should be R instead of R* I think. Else -1 will not be included in H. Correct me if i am wrong.
R* just means the reals without 0. So it does include -1
Based
Is the isomorphism video out yet? my exam is in 3 days ;_;
It comes out tonight! Here's an early link just for you! czcams.com/video/fGqx_-F7zN4/video.html
1) f(e_g.e_g) = f(e_g) f(e_g)
f(e_g) = f(e_g)f(e_g)
Even after applying Group H ooeration, image diesnt change f(e_g) must be an identity element in codomain group H
Hence,F(e_g) = e_h
Wish you created this two weeks ago
Better late than never! Maybe in 7 years I'll have reached my goal of covering a full undergrad curriculum.
Do we know why such math even came into existence? Seems like their could be practical applications.