|Let G and H be groups, and let 0 : G > H be a homomorphism. The set {x E G| 0(x) |e} is called the kernel of 0 and is denoted by ker (0). Show that ker (0) is a subgroup |of G -
|Let G and H be groups, and let 0 : G > H be a homomorphism. The set {x E G| 0(x) |e} is called the kernel of 0 and is denoted by ker (0). Show that ker (0) is a subgroup |of G -
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 7E: Let G be a group and gG. Prove that if H is a Sylow p-group of G, then so is gHg1
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