Visual Group Theory, Lecture 4.3: The Fundamental Homomorphism Theorem
An overview of the fundamental homomorphism theorem (FHT), also known as the first isomorphism theorem, including its statement and significance within group theory.
Professor Macauley
20.2K views โข Mar 20, 2016
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Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagrams before formally stating and proving it. This gives us a 2nd way to prove that two groups are isomorphic, which is often easier than constructing an explicit isomorphism. We conclude by applying the FHT to construct cyclic groups as natural quotients of the integers.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagrams before formally stating and proving it. This gives us a 2nd way to prove that two groups are isomorphic, which is often easier than constructing an explicit isomorphism. We conclude by applying the FHT to construct cyclic groups as natural quotients of the integers.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
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