If there is a group of users and one of the group member has created a Bug then only that member from the group should be able to edit the bug or delete it and no-one apart from that group should perform anything with that bug.
How to achieve that?
You can't quite do this - the permissions do not look at the group of a user named in an issue.
The closest you can get is to have a group nominee. If you add a group-picker field to the issue, you can tell the permissions to use that group-picker field for the permission to edit, and ask your people to always fill in a group that they belong to.
Of course, if you do that, you could also automate it - if you've got access to a scripting or automation app, you should find you can set the group automatically for the user as they create the issue.
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