A group of students - number confusion

I would have used the plural for both verbs. I was told people say "A group of children are playing", not "is playing".
I think "group" is a collective noun, and in American English it's singular: "The team is ready". In British English you might hear "The team are ready", but not in AmE.
But when collective nouns are modified by plural nouns, then everything tends to agree with the plural nouns.

So this thread really confused me... what do you guys think?