It should be believes because group of students is singular

Then why it is 'have begun'?It should be 'has begun' if the subject is 'a group of students' and thus singular?

RC150 wrote:Is this sentence correct->
A group of students, who have begun to study, believes that hardwork is nothing.
I am kind of confused whether it will be 'believe' or 'believes'.Also please explain whether 'have begun' is due to 'students' ,not considering the collective noun 'a group'?

Here is how to tackle this sentence. First remove the modifying clause:

A group of students believes that hardwork is nothing.

The verb believes refers to group.

Next, take a look at the modifying clause:

A group of students, who have begun to study

The verb here is modifying students. Also remember, modifiers always modify the noun directly before the comma.

Here you can see that you have two clauses and they are referring to two different nouns.

I think the main subject is the 'students'.since students is plural,have begun and believe follow