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Homework answers / question archive / 1
1. If alpha is an r-cycle, show that alpha^r = (1). [There's a hint that
If alpha = (i sub 0 ... i sub r-1), show that alpha ^k(i sub 0) = i sub k.]
2. Show that an r-cycle is an even permutation if and only if r is odd.
3. If alpha is an r-cycle and 1<k<r, is alpha^k an r-cycle?
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