There are actually two nonces in mining. One is the 4-byte nonce that each miner chews through from 0 - 2^32. The other is called extraNonce and is inside the first transaction of the block, which is the generation transaction.
My understanding is that whenever the miner requests work from the server, the server will change the extraNonce in the generation transaction so that that miner's work will be unique.
If you look in the first transaction for a block
you can see the extraNonce listed under ScriptSig.
The nonce the miner found is in the block itself
and in this case is 1019732465.