(a) Show that there is a nonabelian subgroup T of S 3 X Z 4 of order 12 generated by elements a,b such that a 6, a 3 b 2 , ba a 1 b (b) Any group of order 12 with generators a,b such that lal 6, a 3 b 2 , ba a 1 b is isomorphic to T ...

a Let us consider the group S3 which has six elements and the cyclic group Z4 which has four elements The group S3 X Z4 has 24 elements which is a mul ...

(a) Show that there is a nonabelian subgroup T of S 3 X Z 4 of order...

Question:

(a) Show that there is a nonabelian subgroup T of S₃ X Z₄ of order 12 generated by elements a,b such that |a| = 6, a³ = b², ba = a^-1b.
(b) Any group of order 12 with generators a,b such that lal = 6, a³ = b², ba = a^-1b is isomorphic to T.