Question

List the elements in each group

(a) ${\mathit{A}}_{\mathbf{2}}$

Short answer

The element in group $A_2$is $\left\{\left(I\right)\right\}$

Step-by-step solution

Alternating group

The set of all even permutations in $S_n$is called the alternating group$A_n$ of degree n

Elements in A2

The group $S_2$has only two elements, which are identity permutation and the permutation that swaps two elements is$\left\{\left(I\right),\left(12\right)\right\}$

Here, the identity permutation has even number of transpositions and the other element (12) has odd permutation.

Thus, by definition, the elements in $A_2$will be$A_2=\left\{\left(I\right)\right\}$

Therefore, the element in group $A_2$is$\left\{\left(I\right)\right\}$