1) "Explain what is meant by is a permutation of . The permutation is 123456 -> 635124, write in cycle notation. Find . How many permutations of are there in the conjugacy class of "
Ok for the first part I don't know how to word it. I know what a permutation does, but I don't know how to call it. sends each element to another? I don't know how to define this. Cycle notation I make it (1 6 4)(2 3 5). Just need a confirmation on this one. Pi^-1, = 452631. The conjugacy classes part I have no idea. I think it means with the same cycle types? But I don't know how to do this?
Also, how many permutations of 6 are there in total? Is it 6!?
2) "The following are permutations of 9. a=(12)(345)(78), b=(1234)(6789), c=(197)(34)(58). Calculate bc. Calculate the conjugate c.b.c^-1.
Does there exist a permutaiton oao^-1 = b, or oao^-1 = c."
Now I remember a rule which says the conjugate sends the part of one to the other, the corresponding part. So a conjugate of something has to have the same cycle type? So for this there would be one for c but NOT a? And for oao^-1 = c, o must be... I forget how to do it?