Question

Prove that (1,2) cannot be written as the product of disjoint 3-cycles.

Answer 1

The pair (1,2) cannot be written as the product of disjoint 3-cycles because it has only two elements.

Step-by-step explanation:

To prove that (1,2) cannot be written as the product of disjoint 3-cycles, we need to consider its cycle decomposition. A 3-cycle is a permutation that sends three elements to each other in a cycle. Since (1,2) has only two elements, it is impossible to decompose it into disjoint 3-cycles.