Will group B and C act as Group A, viewing and editing their own? Or are they just viewers?
Issue security level talks about "who can see an issue", and permission schemes talk about actions performed over the issues.
So, you won't be able to reproduce such behaviour only with Issue Security Level. If Group B and Group C can view a Group A issue, then permission scheme will define if they can edit it or not.
Permissions do not work that way, they don't look at "same group as other user", but you can get there. You don't need issue security levels - that's a simple show/hide operation, which isn't what you're looking for.
What you need to do is actively record the group logging an issue, then you can use that in the permission scheme. Create a group-picker field (you don't need it on screen), and then find or write some code that can detect that someone is in group A and save that in the field during creation. If they are not in group A, then write group B/C (and maybe A) into the field.
The permission scheme can then look at the group-picker field and say "only people in the group(s) named in this field can edit the issue"
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