Permutations and Abelian Group proof.

Where N=10,

http://img502.imageshack.us/img502/1633/ma205assign.jpg

I'm really struggling even starting both questions. (Crying)

Thanks to anyone who can help.

same to find beta





want to find n such that



let's write alpha and beta to see how we can find n

RIGHT, so you can solve it algebraically then sub in N=10 at the end?

EDIT: To clarify, I was starting off with:

Alpha = (10,2) (1,2,8,10)
Beta = (2,3,9) (6,9,10)

but it was the whole cycle notation/product of disjoint cycles thing that really threw me off. I find it very hard to understand.

Quote:

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Originally Posted by MickQ

RIGHT, so you can solve it algebraically then sub in N=10 at the end?

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at least N should equal 26 since you have 23 and N-2, at least N-2=24 , so at least N=26 .

For question 2:

:





Let .

Then

Quote:

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Originally Posted by Amer

at least N should equal 26 since you have 23 and N-2, at least N-2=24 , so at least N=26 .

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The question states that N=10, I wrote it in the initial post. In hindsight, I should've made it a bigger font...really sorry.

okay I asked you

Quote:

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in alpha (12(N-2)N) , 12 is 1 then 2 or it is twelve
and in beta is 23 twenty three or 2 then 3

if 12 is twelve and 23 is twenty three this is the solution

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so it is not twelve and twenty three

I will edit my previous post

Quote:

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Originally Posted by Amer

okay I asked you



so it is not twelve and twenty three

I will edit my previous post

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Right, I understand now. Sorry for not clarifying, here is what it would be:

Alpha = (10,2) (1,2,8,10)
Beta = (2,3,9) (6,9,10)

Icemanfan, even though we the question doesn't state that b^2=1, we can still assume that to be true?

Apologies for the dumb questions, this is really new to me! (Worried)

Quote:

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Originally Posted by MickQ

Icemanfan, even though we the question doesn't state that b^2=1, we can still assume that to be true?

Apologies for the dumb questions, this is really new to me! (Worried)

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for all . This means that if , then . It also means , since by the definition of a group.

is there anything you did not understand

Quote:

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Originally Posted by Amer

is there anything you did not understand

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I was just trying to work it all out using N=10. I ended up with these for Alpha and Beta, but I don't think they are correct:

Alpha: (1,2) (10,8)

Beta: (6,9,3,2,10)

Could you confirm if those are correct?

Quote:

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Originally Posted by MickQ

I was just trying to work it all out using N=10. I ended up with these for Alpha and Beta, but I don't think they are correct:

Alpha: (1,2) (8,10)

Beta: (3,2,10,6,9)

Could you confirm if those are correct?

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alpha is correct, in beta u just made a mitake in the order of two numbers can you fix it.

Quote:

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Originally Posted by Amer

alpha is correct, in beta u just made a mitake in the order of two numbers can you fix it.

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I double-checked and I can't seem to work out where I've gone wrong. Any hints? (Smirk)

Actually, is it (6,9,3,2,10)?