Visual Group Theory, Lecture 4.2: Kernels
14.5 هزار بار بازدید -
9 سال پیش
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Visual Group Theory, Lecture 4.2:
Visual Group Theory, Lecture 4.2: Kernels
The kernel of a homomorphism is the set of elements that get mapped to the identity. We show that it is always a normal subgroup of the domain, and that the preimages of the other elements are its cosets. This means that we can always quotient out by the kernel, and this key observation leads us to the fundamental homomorphism theorem. We concluding with two visual examples: one using multiplication tables, and the other using Cayley diagrams.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/...
The kernel of a homomorphism is the set of elements that get mapped to the identity. We show that it is always a normal subgroup of the domain, and that the preimages of the other elements are its cosets. This means that we can always quotient out by the kernel, and this key observation leads us to the fundamental homomorphism theorem. We concluding with two visual examples: one using multiplication tables, and the other using Cayley diagrams.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/...
9 سال پیش
در تاریخ 1395/01/01 منتشر شده
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