No, there is no such thing as a 'group right' Marxist, etc. Only a group of individuals, each with separate interests that may largely coincide.
And in the case of common resources, then, are we to say that everybody has individual rights?
That's what's led to so many of today's environmental problems.
Or what about eminent domain, in which the interests and rights of a group of people are determined to outweigh those of a single landowner?
Is every member of Congress allowed to impeach the President if he so desires, or mustn't Congress exercise that right as a group?
Common resources are publicly owned. In a democracy, all people own the government. However, it's not like owning something personally, it's more like owning a piece of a corporation, except everyone of voting age has an equal share. Since everyone owns a piece, everyone gets a say in how the land is used, and they can all use them in most cases. It's not the same with privately owned land. Similar concept with the President being impeached - think of the Congress as a board of directors for the corporation and the prez as CEO, just with some slightly different roles. The board and CEO exist because it would be impractical for every individual to be involved in every aspect of a large government.
Now, as far as eminent domain goes, I'll admit that the group seizing the property may have interests, but not necessarily rights to outweigh the right to property. There are cases where eminent domain is used when property is considered 'blighted', but the only blight is a gravel driveway, or the house having only a single bathroom, or there being potholes in the road(which is the local government's responsibility to fix, since roads are public goods) - in cases like this it is only interests, not rights, that bring about the use of this government power. The only valid use for eminent domain, in my opinion, is to take away property that is being used in a way that largely infringes on other's rights. For instance, this happened to my family - our former neighbors had 4 akitas, big fighting dogs, chained up in their yard, and one day two got loose and killed one of our dogs, and then months later they got loose again and bit another of our dogs, both incidents occured on our land. The courts deemed that the woman could not own these dogs because she was irresponsible with them and it harmed our property - they were to be seized by animal control and she wasn't to have dogs anymore. So, eminent domain can only be legitamitely used in cases where the rights of others are being infringed. As with all rights, including property rights, you have certain responsibilities.