Visual Group Theory, Lecture 4.5: The isomorphism theorems
Автор: Professor Macauley
Загружено: 2016-03-23
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Visual Group Theory, Lecture 4.5: The isomorphism theorems
There are four central results in group theory that are collectively known at the isomorphism theorems. We introduced the first of these a few lectures back, under the name of the "fundamental homomorphism theorem." In this lecture, we will see the other three, and we will motivate each one visually. We will prove one of these, sketch the proof of another, and leave the last proof as an exercise. After that, we introduce the notion of a commutator, which corresponds to a "non-abelian fragment" of a Cayley diagram. The commutators generate a normal subgroups, whose quotient yields an abelian group. We state this as a universal property, and close with a few examples.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/...
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