Quiz:Symmetric group:S3

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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.

Review the multiplication table: [SHOW MORE] Review the conjugacy class structure: [SHOW MORE]

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