After reading the following page on false eyes I am not clear as to when a group can be marked as dead.

http://www.ukgochallenge.com/tips/falseyes.html

The first example shows what happens when black captures or white saves the stone in atari, and states that the group is already dead. It goes on to say that the false eye is 'going' to get filled in eventually.

Can the white stones be marked as dead at the end, or only on the condition that the false eye is filled first?

I assumed they could just be marked dead without further play, but the 'going' part has given me some doubt.

You're right - it's simply dead without any further play needed. I see how the wording has confused you, but it doesn't mean that anyone needs to actually fill in the false eye (or indeed do anything else), it's just a way of trying to explain why the group is dead.

All doubt has been removed.

Thanks!

The page in question shows only false eyes in the center of the board. The most common false eyes that you encounter may be on the side, and look something like this:

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . . . . . . .
$$ . . . . . . . . . . . . . .
$$ . . . . . . . . . . . . . .
$$ . . . . . . . . O O O O O .
$$ . . . . O O O O O X X X O .
$$ . . . O O X X X O X a X O .
$$ . . . O X d . c X b X . O .
$$ ----------------------------[/go]

Here 'a' is the only real eye, 'b' is a false eye, and 'c' and 'd' are miai to be false eyes for black lives only if he can play both.

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Note that the general technique for killing a false eye is to atari so that the opponent must fill it. If that can't be done, then the eye still looks false but functions like a real one. One of those bizarre exceptions looks like this:

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . . . . . . . . . .
$$ . . . . . . O O O O . . . . . . . . .
$$ . . . O O O O X X O O . . . . . . . .
$$ . . . O X X X X . X O O . . . . . . .
$$ . . . O X O O O X X X O . . . . . . .
$$ . . . O X O . O O O X O . . . . . . .
$$ . . . O X O O O . O X O . . . . . . .
$$ . . . O X X X X O O X O . . . . . . .
$$ . . . O O O X . X X X O . . . . . . .
$$ . . . . . O X X O O O O . . . . . . .
$$ . . . . . O O O O . . . . . . . . . .
$$ . . . . . . . . . . . . . . . . . . .[/go]

...in which the black stones have two false eyes, but there is no 'back side' from which to attack and force him to fill them, so the stones are still alive.

Also there are sekis in which the false eye cannot be approached:

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . |
$$ . . . . O O O O |
$$ . . . . O X X X |
$$ . . O O O X a O |
$$ . . O X X X O b |
$$ . . O X . X O O |
$$-----------------[/go]

White has not fully surrounded 'b', nor can he do so without putting himself in atari. So it looks false. But black dies if he attacks at 'a', so 'b' keeps white alive.

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Also, even if your group has an eye that really is false from the perspective of life and death, once you have an eye on both sides of the false eye, you can never be forced to fill it in, so you shouldn't. (You get a point for the false eye at the end of the game).

Thanks for the extra information.

Now all I have to do is start playing some games.