Blocking Senders in Google Group
To block or ban unsolicited emails in Google Groups
Note: Owners and group Managers can create filters, report spam or block senders
Start by signing into Google group account and click on the Google group name.

Navigate to the bottom and click on moderation settings.

Select banned users from the left hand column.

Type or paste the senders email address and click ban.

Owners and managers can also create filters to eliminate unwanted or spam email addresses.