Symmetric Multi-Key Decryption
You don't have to use any special asymmetric construct. Just give the group keys and encrypt the file with a unique random key and than encrypt the file key many times using the keys of the permitted users. 

You can give each user multiple keys some of them shared by relevant groups. To prevent encrypting a file with too many keys. These can even be done ad-hoc, assuming groups repeat themselves. you can create a group key encrypt it with the keys of the members and reuse it if you want to give that group access to another resource later.