Math Problem Solver

Let G = A4 and consider the following two subgroups of G:

H={(l),(12)(34),(13)(24),(14)(23)} and J<={(l),(12)(34)}.

(i) Show that K is a normal subgroup of H.

(ii) List all elements in the left and right cosets (12 3)K and K(l 2 3).

(iii) Is K a normal subgroup of A4? Justify your answer.