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## Homework Statement

Is the Cyclic Subgroup { (1), (123), (132)} normal in [tex]A_{4}[/tex] (alternating group of 4)

## Homework Equations

## The Attempt at a Solution

So I believe if I just check if gH=Hg for all g in A_4 that would be suffice to show that it is a normal subgroup, but that seems really tedious. Is there a easier way?

Also how can I figure out what the elements of A_4 are? I know its the even permutations but is there a way to quickly identity which ones it is? How do I visualize it?