Answer to Question #121555 in Abstract Algebra for Priyanka

Question

The set of cosets of (1 2)in S3 is a group with respect to multiplication of cosets.

Answer 1

We have to find coset of (1 2) in S₃ itself

Here (1 2) $\in$ S3

_{therefore , (1 2) S3 ={ (1 2)h : h}$\in$ S₃}

Hence, (1 2) S₃={ I , (1 2),(1 3),( 2 3),(1 2 3),(1,3,2)}

Similarly S₃(1 2)={I ,(1 2),(1 ,3),(2 3),(1 2 3),(1 3 2)} Ans.