beaten up to

[azz]

Can one say
a. He was beaten up to serve as a lesson to the others.

b. He was beaten up to scare the others.

c. They were kidnapped to be slaves.
?

They seem OK to me but isn't there a rule according to which the agent of the second verb should be the agent of the first one?

Many thanks.

[Alan]

A good question, and one to which there is, I fear, no simple or satisfying answer. Yes, ideally, the clause subject and the agent of the infinitive ought to be the same, but there are numerous exceptions, such as the cases you cite (particularly involving passive constructions).

Essentially, such exceptions will be acceptable so long as no ambiguity arises.