I haven't been receiving messages I sent to these groups. I think that
happens because I sent them from my mail program, not from the group
site.
This one I'm sending from the group web interface, and I have turned
on the option "Send me a copy of this message", so I hope it arrives.
If you DO want to receive your own posting to a Google group into your
Gmail inbox, post it from the Group web interface and turn on the
option "Send me a copy of this message". You'll then see what
everybody on the list saw, and your message will be in the mailbox
along with all the other group traffic.
If you DON'T want to receive your own posting in your inbox, post it
from your Gmail account (either from the Gmail web interface or from
your mail program using your Gmail account through the SMTP server at
Gmail). Your message will go to the group and to your Sent Items box
at Gmail. Gmail deletes duplicate messages, so it removes your post
from your inbox. (If you then use your mail program to fetch messages
from the Gmail POP3 server, it won't find your posting there.)
I worked out this information from the second message in the thread at
http://groups.google.com/group/Google-Groups-Basics/browse_frm/thread/1b434fecc5cd07b4/05c3e027dfe11203?hl=en#05c3e027dfe11203
Jim