I had a similar problem today on ubuntu 11.10 64-bit, but my platform is an acer 4755g.
1st of all, let's be absolutely sure that your z570 is using a broadcom
as you can see, z570 supports
1. intel (several diff types)
You do this by
1. opening a terminal
2. running the command
alvinh@ibmsda6:~$ lspci | egrep -i "Atheros|broadcom|intel"
This is my other pc which also run ubuntu 11.10, but the i386 version
02:02.0 Network controller: Intel Corporation PRO/Wireless 2200BG [Calexico2] Network Connection (rev 05)
In your question, you were very specific that you have a BCM4313, so i'm gonna take yr word for it. Let's assume that you've done a lspci & it returns "wireless" & "broadcom" on the same line since this is the only hardware that supports 64bit.
- Now install this package
sudo apt-get install b43-fwcutter
when that's done, goto System Settings (should be on the launcher on the left)
Hardware/Additional Drivers -> Broadcom <- Enable this driver
The rest is the same as previous releases of ubuntu; on the top right-hand, click on the LAN & configure your wireless lan info.
Good luck Alex; this is as best as i can do for you bec it's exactly what i did!