Generics & Inheritence

Question

I'm designing an object model which needs a few constraints and I'm not sure how exactly to do what I want in C#, any help is appreciated.

Basically

Class A {...}
Class B : A {...}
Class C : B {...}
Class AGroup : Collection<A> {...}
Class BGroup : AGroup {...}
Class CGroup : BGroup {...}

The feature I need is to make sure that BGroup's collection only has B objects in it, but retains all the methods and members from AGroup.

While CGroups's collection only has C objects in it but has both A and B methods and members accessible.

Strong typing which gets stronger each level of inheritance.

Is this possible?  
Thanks in advance,
Tyler Copple