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I have shared a link in a secret facebook group. The link is a facebook page of someone. Does this person get a notification of the mention?
Pages don't get any notification in a group even if you tag them in the secret group. I've just tagged one of my page in a secret group and I didn't receive any notification. Just to test it ;)
Same applies for a tag of a person in a secret group.
No s/he doesn't. Unless you tag him/her, s/he won't.
Required, but never shown