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

From Groupprops
Jump to: navigation, search
(Created page with "See symmetric group:S3. We take the symmetric group on the set <math>\{ 1,2,3 \}</math> of size three. ==Elements== See element structure of symmetric group:S3 for full...")
 
(Elements)
Line 5: Line 5:
 
See [[element structure of symmetric group:S3]] for full details.
 
See [[element structure of symmetric group:S3]] for full details.
  
Review the multiplication table: <toggledisplay>{{#lst:element structure of symmetric group:S3|multiplication table}}</toggledisplay>
+
Review the multiplication table in cycle decomposition notation: <toggledisplay>{{#lst:element structure of symmetric group:S3|multiplication table}}</toggledisplay>
 
+
<br>
 +
Review the multiplication table in one-line notation: <toggledisplay>{{#lst:element structure of symmetric group:S3|multiplication table in one-line notation}}</toggledisplay>
 +
<br>
 
Review the conjugacy class structure: <toggledisplay>{{#lst:element structure of symmetric group:S3|conjugacy class structure}}</toggledisplay>
 
Review the conjugacy class structure: <toggledisplay>{{#lst:element structure of symmetric group:S3|conjugacy class structure}}</toggledisplay>
  

Revision as of 14:45, 8 October 2011

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 in cycle decomposition notation: [SHOW MORE]


Review the multiplication table in one-line notation: [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