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'There was a group of people, each pointing in a different direction.'

1) Here, would you say the italicised words are an adjective phrase? Or a non-finite dependent clause (reduced relative clause)? Why I am confused whether it is one or the other is because a non-finite clause can sometimes have no subject...even though it is a clause, so I thought that maybe this was a non-finite clause and not a phrase...

2) And is this sentence grammatical? Everything after 'people' seems weird..with the comma joiningthem together..
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3) I often see constructions like this where they omit the verb (each was pointing) so that it is no longer a clause and insert a comma (now that there it isn't a clause, a comma is permissible). So is this fine?

There was a group of people. Each were pointing in a different direction.

BECOMES: 'There was a group of people, each pointing in a different direction.'

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If I write it with a relative clause.......

'There was a group of people who were/was each pointing in a different direction'

4)Each is a singular indefinite pronoun, so I thought it would be 'was'. But, I think the subject is not 'each,' but 'who', which is plural (group of people). So it is 'were'. Is this correct?

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Thanks a lot in advance.
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I'm sure you realize "group" may be singular or plural, but not both. If you're going to refer to actions by the individuals, you must use the plural when referring to "group."

Are you not hearing the "each" phrase as an appositive?
Comments  
Don't know the term to answer question 1. Yes, the sentence is perfect English. If you say, "There was a group of people, who were each pointing in a different direction," that is not correct because group is singular, so you couldn't say "were." You could break it up and say, "There was a group of people. Each was (here "individual is implied) pointing in a different direction," that would be fine too.

Your restatement: "There was a group of people. Each pointing in a different direction" doesn't work. You need a verb, as above.

English is funny. Just accept it!
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'You need a verb, as above'

There is a verb. 'Was' is the verb; it is the verb in the relative clause.

Cheers
 Avangi's reply was promoted to an answer.
'There was a group of people, each pointing in a different direction.'

Hi, yes, I did think it may be an appositive; however, I also thought it wasnt exactly saying who the group was as much as it was saying what the group was doing. Thus I believed, with uncertainty, that it was an adjective phrase with pointing as the head of the phrase (present participle).

But once again, I am not sure, haha.

I sometimes feel the answers to such questions are arbitrary, but I'm sure this is untrue; if only it were a matter of personal opinion, that would be nice!
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I'm sure you read CJ's last post in the Clause thread. That seems to make it clear that there's no one official way to look at things.