I have read she did not notice it but this is hard to belive. The 3 oathes should not have allowed them to kill any man who is not proven to be a darkfriend. Possibly a BA but why would not some else say something about it?

I just started re-reading TSR, I'll have to read that scene closely.  Elaida had to have known who did it, since Siuan vows to Elaida that she'll pay for it when she finds Alric dead.

They can kill without the power just as easily as a non-channeler. I never got why Siuan didn't notice her warder being killed, but the Aes Sedai that voted to have her demoted would have taken out the warder to avoid having him go on a rampage. They could have just used air, though. Unless there's a short window of time where the Aes Sedai won't feel the warder's death then it would just have served to warn Siuan. Or maybe he attacked the Aes Sedai when they captured Leane.

The oaths prevent them using the power to kill him. He can be killed by the aes sedai with a knife or the warders. It was said the shock made her not notice so he was probably killed the instant they shielded her.

Alric was not killed using the One Power, he was stabbed.  In the back.  With a knife ... ah, such treachery.

 

Here is the quote from Jordan's Blog:

 

For Roland Arien, a lot of people have asked questions about Alric’s death.  I should have made matters plainer.  As I envisioned it, Alric, having sensed Siuan’s extreme shock, came running to her and arrived just in time to be stabbed just before Siuan was taken into the anteroom.  She should have sensed the knife going in, but that was masked by her shock.  When she sees him lying there, he is dying, though not yet dead.  As I said, I should have made it plainer.

 

http://www.dragonmount.com/RobertJordan/?p=27

 

 

 

That quote is pure gold. Never seen it before.

That does clear up a whole lot. That whole scene never worked for me, but now it makes sense.