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Provethatife : G -+ His a homomorphism and A is a subgroup ofG, thene(A) isa

Chapter 21, Problem 21.9

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QUESTION:

Provethatife : G -+ His a homomorphism and A is a subgroup ofG, thene(A) isa subgroupofH.

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QUESTION:

Provethatife : G -+ His a homomorphism and A is a subgroup ofG, thene(A) isa subgroupofH.

ANSWER:

Step 1 of 4

Let ,where is a group. Then H is called a subgroup of G (denoted as )

If it is a group with ‘*’. Mathematically,  iff for ,  

A mapping is called a homomorphism from A onto B, if

 for all

If is homomorphism then

 

, the image of , is a subgroup of H (It is called homomorphic image of G)

If  is one-to-one, then

 

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