By what you said about the order, . So, to start with, you should work out 9000 and -21 modulo 11. Can you see why you would want to do this?
I'm sure there is a quick and straightforward method for answering this question. But I can't find it in my textbook.
Here's what I know:
in the array notation would be:
and can be written as a product of disjoint cycles:
Since it's only one cycle of length 11, the order is lcm(11)=11
I'd be thankful if anyone could show me what method to use to find and .
Well this is what I mean:
Now writing those numbers modulo 11 we have:
Since the 4 and 9 have been repeated twice, the one cycle doesn't make any sense! Do you see the problem? I tried to break this up into new disjoint cycles but that wouldn't work either...
No, that is not what means! means the permutation done twice. maps 1 into 6 and then 6 into 7 so maps 1 into 7. maps 7 into 3 and then 3 into 11 so maps 7 into 11.
In cycle notation, starts "(1, 7, 11, ..."
Now writing those numbers modulo 11 we have:
Since the 4 and 9 have been repeated twice, the one cycle doesn't make any sense! Do you see the problem? I tried to break this up into new disjoint cycles but that wouldn't work either...[/QUOTE]