Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
18.5 هزار بار بازدید -
8 سال پیش
-
Visual Group Theory, Lecture 4.3:
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/...
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/...
8 سال پیش
در تاریخ 1395/01/01 منتشر شده
است.
18,542
بـار بازدید شده