What's wrong with 'the students' cheating displeased themselves'?

Question

The students’ cheating displeased themselves.

It seems to make sense, but a book says it’s ungrammatical. I can’t find any reason for it. What’s wrong with the sentence?

Answer 1

You have to distinguish between a reflexive pronoun employed as a sentence constituent and the same pronoun employed as an emphatic appositive to its referent.

In your sentence, themselves must, by its position, be the direct object of the verb displeased, and therefore must refer to the sentence's subject, cheating. But that is a) singular, which is a grammatical error, and b) incapable of pleasure or displeasure, which is a semantic error.

What the sentence is probably trying to say is:

The students' cheating displeased the students themselves.

Here students is the direct object, and themselves is emphatic, indicating that the subject and object students are the same students.

Answer 2

The subject of the sentence is cheating. It’s singular and themselves is plural, but in any case it’s hard to imagine in what circumstances cheating might displease itself.

What the sentence seems to be trying to say is that the students cheated and the fact that they did so displeased them. The most economical way of saying that is The students were displeased by their own cheating. Even so, displeased is not the best choice here. It might be more accurate to say The students were ashamed of their cheating.

Answer 3

The word in question is cheating. Formally, it may be a gerund or a verb in present participle form. Let's see what happens in each case:

• Suppose it's a gerund, e.g. "students' cheating" is a subject of the phrase. If so, we have to admit that cheating does something to themselves. But cheating is not a person, and metaphorical impersonation does not look convincing here. Also, cheating stands for phenomenon of cheating which is singular according to English grammar, so it does not work well with displease themselves.
  Hence, this variant is not grammatical;
• Suppose it's a verb in present participle. Then we need a subject. Students' is a possessive, it can't be a subject alone; also, present participle requires a helper verb, are.
  Therefore, this variant is not grammatical as well;

To make the phrase grammatical:

• If you go with a gerund, refer @Barrie's and @StoneyB's answers;
• To me, a verb looks more natural. Here's my take:

The students who are cheating displease themselves.