Both the groups you found out are isomorphic to the second group given in Rosen.

0 votes

reference:Rosen

i think two more abelian groups are possible .

1 and 3 are given ,2 and 4 also exist .if i m wrong let me know ,thank you.

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Please explain what is isomorphic group..i have seen this for many times but haven't studied about it..

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Is group theory given in Rosen Prateek Raghuvanshi ? I never found it . :(. Can you plz tell me the edition exactly or the reference for reading group theory. Thanks

3 votes

Best answer

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@Utkarsh , can you please explain how you created the function mapping between 2 sets. here $f$ is not defined . so how you mapped the element from one set to another. Please explain :)

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yes $f$ is not defined, i mapped the elements with same behavior in A to same behavior in B and C to show one to one correspondence in the given groups

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Sorry.. I am still not getting the mapping. Can you please explain a little bit about mapping for elements b And c from set A to set B ?

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check the mapping and take group B's table and map the elements based of the mapping $A \rightarrow B$ you'll get the same mapping back of A

or vice versa, take A's table and interchange elements d and c you'll get the same table back.

Behavior of group B's d is same as group A's c

and

Behavior of group B's c is same as group A's d

or vice versa, take A's table and interchange elements d and c you'll get the same table back.

Behavior of group B's d is same as group A's c

and

Behavior of group B's c is same as group A's d