"Your email delivery (subscription) settings relate to receiving emails for messages that are posted to the group.? If you choose to send a message direct to a member from either your own or group owner address, they don't apply because that message isn't posted to the group."
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The person asking me if I knew a way to push an email to someone set as No Mail wanted to send an email out to everyone in her group.
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I've sent her back all the answers and she is now happy.