Yes, the permission schemes are designed for this.
At the very basic level, they can do a simple "if in group X, allow action Y", but they're a lot more powerful. You can do things like "if in role X for this project, then allow Y", and then put groups into roles.
However, I suspect your question may be more complex than the standard permissions. If my instincts are right, could you explain your requirement futher?
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