Can I say: "a group of ten-year-olds" or should I add the noun for example students "a group of ten-year-olds students"? Thank you in advance for your answer.
"A group of ten-year-olds students"
... is not correct. It should be:
A group of ten-year-old students.
However, your original example is correct:
A group of ten-year-olds.
In the first example you are describing a group of students (plural), and you are merely adding the qualifying detail that each of them is ten years old.
In the second example where you omit the word students you are actually describing the group as "ten-year-olds", and the expression becomes a noun which is why it ought to be plural.