Hello everybody,
Mohammad,the same problem bothered me too.I've also met the phrase "by+agent" in parsing sentences and I don't find it helpful.The main reason is that I've learned grammar on the basis which Quirk founded and I absolutely agree that introducing other terms,like "by-agent" in this case,does not make things clearer,on the contrary.Speaking from the viewpoint of a learner and not a grammar proffessional,in the sentence type like you've quoted:
"The computer has been purchased by the group."
the element "by the group" doesn't sound "adverbially" (it doesn't respond well to the question "how"and would be a better answer to the question "who"),still I wouldn't introduce some new concept in the nomenclature which Quirk established.And I have two reasons for such opinion in this particular case:
1. First,the term tells about the semantics of the phrase and not about its syntactic function in the sentence.I think that analysis of a sentence require some automation and some sequence of steps,carrying it out strictly step by step,the first step being a syntactic analysis.I consider this first step as a bird's eye view,or a rough sketch of the sentence.That mean the first thing you do is a technical job of identifying sentence parts and,if required,dissecting that parts all the way to the words constituents in that sentence.Then you can analyse further what exactly some part is by its form,what is its semantics etc.In my opinion,implicating semantic terms and elaborations in the syntactic analysis of the sentence structure is a highway to confusion.
2. Secondly,even if other term was chosen it still means enlarging the structure of five elements which Quirk has given (not four,you've missed "object" as a element of a sentence structure)and it complicates things.Using that logic,the Quirks structure could be enlarged with a lot more elements for every unfitting exception.
I think that one simple structure as Quirk has established enables an ESL learner to acquire automation similar to native speakers.Knowing logical slots in which words fit makes easier incorporating new vocabulary and gives a basic orientation to an ESL learner i.e a roadmap to things which he should focus on in his learning.An ESL learner should always have in his mind that grammar is a tool and a very basic tool in acquiring any language.It is valuable as much as you can use it effectively.
As a conclusion,I think that compared with the immensity of other fields which Quirk's conception brilliantly elaborate some questionable issues can be ignored.It would be like not seeing the wood for the trees.In a mass of different approaches and conceptions in the field of english grammar I chose Quirk's grammar as the most convinient and useful in the store.And although I take every opportunity to learn something more and different on grammar,I keep away from mixing its conception and terminology too much with other to avoid confusion.
P.S In "A Student's Grammar of the English language" ,semantic roles of adverbials are elaborated in chapter 8 and "by+noun" construction is under "process" role of adverbials ,subclass "agency".
Best regards
Velimire