# abstract algebra

• October 14th 2007, 11:29 PM
jenjen
abstract algebra

Show that if σ is a cycle of odd length, than σ² is a cycle.
• October 15th 2007, 05:44 PM
ThePerfectHacker
Quote:

Originally Posted by jenjen

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

Not true.
• October 15th 2007, 11:18 PM
jenjen
really? but I was told to show that according to my math book.
• October 16th 2007, 03:54 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.