Singular subjects such as each and either are
Subjects such as each, either, neither, and
everyone, followed by prepositional phrases
containing plural words ("each of the men," "either
of the children"), can be thought of as really
meaning "each one" and "either one."
These are always singular.
Thus, we use singular verbs with them:
Each of the men is applying
for the promotion.
Either of the children sings
Neither of the applicants was
qualified for the position.
Something is wrong here.