The existing answers already correctly state that there are of course things that you are not allowed to publish on, period - for example state secrets, or national security related research. Depending on how strict you are about the word "allowed" some industrial research that is covered by a Non-Disclosure Agreement may also fall under this umbrella.
are there...any restrictions [on] what...research can be published.
Yes. For example, national security laws restrict the publication of certain works and legality of human/animal experimentation restrict others.
As I haven't seen either code, and as a university professor myself, based on what you have mentioned, I would recommend that you consult with the GPL licensing authority.... They can decide about the proper respond both legally and ethically
What that person did, was not just plagiarism, but also copyright infringement. They took a GPL licensed work (legal), modified it (still legal), published it, but not under the GPL license (copyright infringement), and claimed it as their own work (plagiarism).
If you wanted to be nasty, you could tell the original author of the code about this, and if ...
With the caveat that I am not a lawyer, the answer is "no".
code A, which is GPL-licensed
code B, which is a derivative work of A and not GPL-licensed.
The GPL license requires that all derivative works are also GPL-licensed. As B does not carry the GPL license, it is a copyright violation and (depending on jurisdiction) it is probably illegal ...