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In Groups.io each group has an owner email address. Each moderator has a subscription option to control receiving messages sent to the owner address. 
The owner-email address is listed at the bottom of the home page for each group.
Owners can set up preferences for receiving email to this address -  set it to "None" or (from) "Subscribers only". 
The control is at the bottom of the Subscription page in each group (of which you moderate or own).
Go to Subscription, and scroll down to see the controls for Owner Email.