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Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 22E: Exercises 22. Let be a finite cyclic group of order with generators and . Prove that the mapping...
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5. Let G be a finite group and let G' be a group. Let : G → G'
be a homomorphism. Prove that o[G]] divides |G|. [Ilint: Use the
Fundamental IHlomomorphism Thcorem.]
Transcribed Image Text:5. Let G be a finite group and let G' be a group. Let : G → G' be a homomorphism. Prove that o[G]] divides |G|. [Ilint: Use the Fundamental IHlomomorphism Thcorem.]
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Step 1

Let,

G be finite group and order of group G is n and n is finite.

Let,

G' be a group such that  ϕ: G ⟹ G'

be an group homomorphism.

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