0 votes 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. Set Theory & Algebra group-theory + – Prateek Raghuvanshi asked Oct 13, 2018 Prateek Raghuvanshi 1.0k views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments Mk Utkarsh commented Oct 14, 2018 reply Follow Share Pawan Kumar 2 It's in Indian edition 0 votes 0 votes Pawan Kumar 2 commented Oct 14, 2018 reply Follow Share Thanks brother Mk Utkarsh 0 votes 0 votes ankitgupta.1729 commented Nov 1, 2018 reply Follow Share @Prateek, Can you please explain the mapping for elements b and c from set A to set B in the given answer ? 0 votes 0 votes Please log in or register to add a comment.
Best answer 3 votes 3 votes Isomorphism : A group homomorphism that is bijective. We proved that all 3 groups are homomorphic as well as isomorphic. Note: I rearranged the elements of table to show the similarities between all 3 tables. Mk Utkarsh answered Oct 13, 2018 selected Oct 13, 2018 by Prateek Raghuvanshi Mk Utkarsh comment Share Follow See all 6 Comments See all 6 6 Comments reply ankitgupta.1729 commented Oct 31, 2018 reply Follow Share @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 :) 0 votes 0 votes Mk Utkarsh commented Oct 31, 2018 reply Follow Share 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 0 votes 0 votes ankitgupta.1729 commented Oct 31, 2018 reply Follow Share 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 ? 0 votes 0 votes Mk Utkarsh commented Nov 1, 2018 reply Follow Share 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 1 votes 1 votes ankitgupta.1729 commented Nov 1, 2018 reply Follow Share got it. Thank you :) 0 votes 0 votes Magma commented Nov 1, 2018 reply Follow Share very well explained :D 0 votes 0 votes Please log in or register to add a comment.