Julia, If you are the owner or manager of the group, you can set a custom header that is appended to all the emails posted by anyone to the group. For example if I post an email with the subject - Forum Meeting Wed 6PM, then the group mail system can automatically append [Julia Brown Group] Forum Meeting Wed 6PM in the subject (assuming you have set that as the text to be appended).
Once you do this, then all the members have to add a filter in their email systems that identifies emails with that in the subject as "Safe"
Alternately, if you have allowed the emails to be sent as if originating from the group, then the sender will be
Julia-...@googlegroups.com (assuming your Google Group is named Julia Robert) irrespective of the person who has sent the email - and all in the group need to add this email address in their safe senders list.
All the best, have fun and hope the above helps.
Joe