Currently Being ModeratedNov 10, 2012 4:06 PM (in response to linda2009)
That's not quite true. You need to map the Trash mailbox under the Gmail imap folder to the main trash mailbox on the Mac first. That should set it to store messages on the server. Then trash messages will be available on all computers. When you delete the trash on the mac, it deletes it on the server.
You aslo have to set this correctly at the gmail website. Expunge message when deleted from the last visible imap folder. Also set to move message to trash when deleted and not archive.