# abstract algebra

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• Oct 14th 2007, 10:29 PM
jenjen
abstract algebra
Please help me with this problem:

Show that if σ is a cycle of odd length, than σ² is a cycle.
• Oct 15th 2007, 04:44 PM
ThePerfectHacker
Quote:

Originally Posted by jenjen
Please help me with this problem:

Show that if σ is a cycle of odd length, than σ² is a cycle.

Not true.
• Oct 15th 2007, 10:18 PM
jenjen
really? but I was told to show that according to my math book.
• Oct 16th 2007, 02:54 PM
ThePerfectHacker
Sorry, I was wrong.
I think we need to show,
$(a_1,...,a_n)^2 = (a_3,...,a_n,a_1,a_2)$
Where $n>1$ is odd.