Question

List all of the partitions of 6. For each partition π , give a permutation σπ is in S6 whose cycle structure is given by that partition. For each σπ , list all of the powers of σπ and indicate the order of σπ.

Answer 1

Answer:

Each partition of 6 corresponds to a conjugation class in S_6.

For instance, the partitions of 6 can be described as,

1. 6 : example cycle type (1, 2, 3, 4 ,5 ,6)

2. 5+1 : example cycle type (1, 2, 3, ,4 ,5)(6) = (1, 2, 3, 4 ,5)

3. 4+2 : example cycle type (1, 2, 3, 4)(5,6)

Since P(6)=11, there are 11 conjugation classes in S_6. Note that each cycle type in S_6 represents a conjugation class(partition) in S_6.

Step-by-step explanation: