Is A3 a Normal Subgroup of S3?

[e179285]

H=A₃= {(1),(1 2 3),(1 3 2)} and

G=S₃ ={ (1),(1 2 3),(1 3 2),(1 2 ),(1 3),(1 2 3) }

Is H is normal subgroup of G ?
I try g=(1 2 3 ) for gH=Hg but gH≠Hg for all g ε G.In this situation,H is normal subgroup pf G?

 

[Dustinsfl]

I haven't check your assertion, but in order for H to be a normal subgroup of G, ##gH = Hg## for all ##g\in G##.

If you have ##gH\neq Hg## for some ##g\in G##, then H isn't a normal subgroup of G.

 

[micromass]

What is [G]?? What does that tell you??