Question

Question: (a) Show that _{$D_3\cong S_3$} [Hint: is described in Example 6 of Section 7.1 or 7 .1.A. Each motion in permutes the vertices; use this to define a function from $D_{3}to{S}_3$to .]

Short answer

Answer

It is proved that $D_3\cong S_3$.

Step-by-step solution

 Step 1: Isomorphic Groups

Two groups G and H are said to be isomorphic if there exists an isomorphism F from G onto H .

Show that D3≅S3

The labelling of vertices in the given example shows the mapping with the following table.

By construction, this map is a homomorphism and it can be directly verified that it is a bijection. Therefore, it is proved that $D_3\cong S_3$.