I found this sentence:
I am convinced that not only could I control a group of people effectively, but the group would also benefit from my skills.
Why is this word order correct: "could I" (auxiliary verb + subject)? Which clause structure/rule is this?
When used in this way, "not only" requires an auxiliary verb and sub-aux inversion. Thus, for example, all of the following are correct:
Not only could I control . . .
Not only did I control . . .
Not only was I controlling . . .
It won't work, however, with a non-auxiliary verb:
*Not only controlled I . . .
