hmmm..ok..that makes a little more sense to me. Maybe I can try to look at this prob again and see what I can get. Thanks for being so patient...this group theory is kicking my b**t ; )
yep...word for word...now the book defines a transposition as "a cycle of length 2"...so I guess the problem might be saying to show that the most 2-cycles a permutation can have is m-1...is that right?
This probelm is from Fraleigh's 4th ed...stated as follows
Prove the following about S_n if n>=2.
Every permutation in S_n can be written as a product of at most n-1 permutations.
The m permutations phrase I picked up while trying to get more information about this idea. Maybe it's...
yes...I suppose I mean a cycle of length m...that would be the m permutations I think. I'm really floundering when it comes to this permutation stuff...thanks.
ok...I had found one that said m>=2 but another for m>=3. Let's go with 3...then for instance (1 3 2) for S_5 can be written as a product of at most 2 transpositions...i.e. (1 3)(1 2) or a couple of others. I see this...but I can't figure how to prove for the nth term.
Can someone help me? I need to prove that for m>=2, m permutations can be written as at most m-1 transpositions. I can't figure this out for the life of me! thanks in advance :confused: