3. Among $m$ students, it is known that in any group of three, two of them know each other, and in any group of four, two of them do not know each other. Then the maximum value of $m$ is $\qquad$
3. 8 .

When $m=8$, the requirement is satisfied.
It only needs to prove: $m \leqslant 8$.
First, prove that the following two scenarios are impossible.
(1) If a student $A$ knows at least 6 people, by Ramsey's theorem, among these 6 people, there exist 3 people who either all know each other or all do not know each other. If it is the former, then $A$ and these 3 people form a group of 4 people who all know each other, which contradicts the given condition; if it is the latter, this contradicts the given condition that among any 3 people, there are 2 who know each other.
(2) If a student $A$ knows at most $m-5$ people, then at least 4 people do not know $A$, thus, these 4 people all know each other, which contradicts the given condition.

Secondly, when $m \geqslant 10$, either (1) or (2) must occur, which is impossible.

When $m=9$, to make (1) and (2) not occur, each student must know exactly 5 other people, thus, the number of friend pairs (pairs of people who know each other) generated by these 9 people is $\frac{9 \times 5}{2} \notin Z$, which is a contradiction.
In summary, the maximum value of $m$ is 8.