Kernels of Homomorphisms in Abstract Algebra

Support the production of this course by joining Wrath of Math to access all my Abstract Algebra videos plus lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 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) ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● 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