Here are some example sentences that show my thought process:
Some cats are playing with each other.
Okay, it seems obvious that "some" is a determiner.
A number of cats are playing with each other.
Likewise, "a number of" must also be a determiner. "Number" can't possibly be the head of the noun phrase, that doesn't make any sense. You wouldn't say, "A number is playing with each other."
(?) A group of cats are playing with each other.
Here I might get in trouble for subject/verb agreement, but if I assume that "group" is the head of the noun phrase, I get the following nonsensical statement:
(!) A group is playing with each other.
This doesn't make sense to me because "with each other" has the semantic implication that the subject must be plural, and yet "group" is not plural. Perhaps this is specific to my dialect (American English).
My sense is that "a group of", "a number of", and "some" can all function as determiners, and that the only reason that "a group of" is under dispute is because "group" can also function as a subject, meaning that both of the following sentences are grammatical:
A group of cats is causing a problem. (Head: "group")
A group of cats are causing a problem. (Head: "cats")
Is this analysis correct?