there are some mistakes in your sentences:
a group of people was being very loud. Another person near that particular group was also being equally loud. (this is the correct way of saying it).
"being" here is the gerund that we use for continuous actions. So that group of people wasn´t just loud at some point, but they started to be loud and kept on being louder.
"a group of people was very loud" means at some point we could notice that a group of people was loud.
A group of people were being very aloud. The other person arround that partucular group was also being equally loud.
Could you please explain the grammatical rule of "being" here?
If I Just write "A group of people were very aloud." Is it going to change the meaning of the sentence?
Let me start by offering a 'better' sentence but retaining the meaning.
A group of people were making a lot of noise. Another person, near the group, was equally noisy.
'Being very loud' where 'being' is indicating what the group 'were doing' is an adjective; I am being pedantic; you are being curious. 'Being' is the explanatory adjective - without that in each of those cases the meaning would infer a fixed state, whereas with it the meaning infers 'now', not necessarily at any other time.
Note the correct noun is loud - aloud is an adverb. So your last sentence would be correct using 'loud'.
Now the second sentence, corrected: the other person (around is wrong; one person cannot stretch around a group of people - impossible - but a group of people could be around one person, in other words encircling him/her) near to, close to, at the side of, alongside that particular group was equally loud, was also loud, was being equally loud. In the sentence 'also' and 'equally' are really unnecessary; one or the other will suffice.
Thank you for the explanation. I always make errors in subject very agreement.
If I change the sentence to the following form is it correct?
A customer came to the information desk and complained that there was a group of customers who were being very loud and they were uttering slangs at each other.
This -in subject very agreement - does not make sense, so please amend this.
The sentence should be:
A customer came to the information desk to complain that a group of customers were being very loud, (using slang) swearing at each other.
Note: came to the information desk (for a purpose) to complain, not 'and complained' which infers that he came there for something additional to complaining.
That (there was - unnecessary) a group (who) were uttering (slangs - is a plural we do not use; singular 'slang' is jargon, incorrect language and I think you meant 'swearwords').