# Difference between revisions of "Quiz:Symmetric group:S3"

See symmetric group:S3. We take the symmetric group on the set $\{ 1,2,3 \}$ of size three.

## Elements

See element structure of symmetric group:S3 for full details.

1 What is the number of non-identity elements of the symmetric group of degree three?

 2 3 4 5 6

2 How many elements are there of order exactly three in the symmetric group of degree three?

 2 3 4 5 6

3 What can we say about the order of the product of two distinct elements, each of order exactly two, in the symmetric group of degree three?

 The product must be the identity element The product must have order two The product can have order either 1 or 2 The product must have order three The product can have order either 1 or 3

4 What can we say about the order of the product of two distinct elements, each of order exactly three, in the symmetric group of degree three?

 The product must be the identity element The product must have order two The product can have order either 1 or 2 The product must have order three The product can have order either 1 or 3