# Proving a set of permutations is a group

• Mar 12th 2011, 08:07 PM
manygrams
Proving a set of permutations is a group
Hey there,

I'm trying to prove a set of permutations is a group, but the textbook isn't very clear how to do so.

G={id, (1 2), (1 3), (1 4)}; operation in S_4

If anyone can offer any words of advice, that would be much appreciated.
• Mar 12th 2011, 09:34 PM
abhishekkgp
Quote:

Originally Posted by manygrams
Hey there,

I'm trying to prove a set of permutations is a group, but the textbook isn't very clear how to do so.

G={id, (1 2), (1 3), (1 4)}; operation in S_4

If anyone can offer any words of advice, that would be much appreciated.

the product of $(1\,2)$ and $(1\,3)$ is $(1\,3\,2)$. this does not lie in $G$.Hence $G$ is not closed under multiplication. How can $G$ be a group?