Write $(12), (13),(14),(23),(24),(34)$ as product of two permutations, each with order 2.

Asked Sep 26 '17 at 11:06

Active Sep 26 '17 at 11:06

Viewed 83 times

So in my book it's stated that every element of $S_4$ can be written as a product of two permutations, each with order 2.

I tried to do this, but got stuck with the elements $(12), (13),(14),(23),(24),(34)$, so basically the transitions.

Any tips on how to write the transitions in the mentioned form?

asked Sep 26 '17 at 11:06

Fruitdruif

8

$(12)=((12)(34))(34)$ – Sep 26 '17 at 11:09
1

Note that in $S_{n}$, for any $n > 3$, every permutation can be written as the product of two involutions, i.e. of two elements of order $2$. See for instance this post. – Andreas Caranti Sep 26 '17 at 14:49

0 Answers0