Kernels of Homomorphisms in Abstract Algebra
Explore the concept of kernels in homomorphisms as part of the Abstract Algebra course. Join Wrath of Math for full access to all Abstract Algebra videos and lecture notes at the premium tier!

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10.4K views β’ May 19, 2023

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We introduce kernels of homomorphisms. We give the definition of kernel in group theory, an example of a kernel of a homomorphism onto the additive group of real numbers, then finish by proving the kernel of a homomorphism is a normal subgroup of the domain group of the homomorphism. #abstractalgebra #grouptheory
Group Homomorphisms: https://youtu.be/rJpu22jMeIY
Basic Properties of Homomorphisms: https://youtu.be/7tRDyAbgrJ8
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Fundamental Homomorphism Theorem: (coming soon)
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0:00 Intro
0:33 Definition of Kernel of a Homomorphism
1:26 Example of a Kernel of a Homomorphism
5:08 Proof Kernel is a Normal Subgroup
10:21 Outro
https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
π Check out the coolest math clothes in the world: https://mathshion.com/
Abstract Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz
Get the textbook! https://amzn.to/45IvVgH
Business Inquiries: wrathofmathlessons@gmail.com
We introduce kernels of homomorphisms. We give the definition of kernel in group theory, an example of a kernel of a homomorphism onto the additive group of real numbers, then finish by proving the kernel of a homomorphism is a normal subgroup of the domain group of the homomorphism. #abstractalgebra #grouptheory
Group Homomorphisms: https://youtu.be/rJpu22jMeIY
Basic Properties of Homomorphisms: https://youtu.be/7tRDyAbgrJ8
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Fundamental Homomorphism Theorem: (coming soon)
β DONATEβ
β Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons
β Donate on PayPal: https://www.paypal.me/wrathofmath
Follow Wrath of Math on...
β Instagram: https://www.instagram.com/wrathofmathedu
β Facebook: https://www.facebook.com/WrathofMath
β Twitter: https://twitter.com/wrathofmathedu
0:00 Intro
0:33 Definition of Kernel of a Homomorphism
1:26 Example of a Kernel of a Homomorphism
5:08 Proof Kernel is a Normal Subgroup
10:21 Outro
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Video Information
Views
10.4K
Likes
257
Duration
11:04
Published
May 19, 2023
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4.6
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