Quiz:Symmetric group

From Groupprops
Jump to: navigation, search

Elements

1,1,2,3,3
1,3,4,4,12
1,3,6,6,8
1,1,4,4,4,4,6
1,2,2,2,3,4,4,6

2 Given an element picked uniformly at random from symmetric group:S4, what is the probability that the square of this element is the identity element? See element structure of symmetric group:S4#Conjugacy class structure.

1/4
5/12
1/2
7/12
2/3

3 What is the probability that two elements of symmetric group:S3, picked uniformly at random and independently (so they may be equal) generate the whole group? See generating sets for subgroups of symmetric group:S3.

1/2
2/3
3/4
5/6
1

4 What is the smallest value of n such that the symmetric group of degree n contains an element of order 6?

3
4
5
6
7

5 What is the maximum possible size of a conjugacy class in the symmetric group S_n of degree n, for n \ge 3?

n!
(n - 1)!
(n - 2)!
n!/(n - 1)
n!/(n - 2)