If G and H are groups with identities 16 and ¹H, respectively, and f:G ---> H is a homomorphism, then the kernel öf f is a. f(¹G) b. f(G) c. f-¹ (H) d. f-¹(1g) e. ¹H

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 38E
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If G and H are groups with identities lc and 1, respectively, and
f:G ---> H is a homomorphism, then the kernel öf f is
a. f(¹g)
b. f(G)
c. f-¹ (H)
d. f-¹ (¹) e. ¹H
Transcribed Image Text:If G and H are groups with identities lc and 1, respectively, and f:G ---> H is a homomorphism, then the kernel öf f is a. f(¹g) b. f(G) c. f-¹ (H) d. f-¹ (¹) e. ¹H
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