The root word "apply" means to put something to use, to bring something into operation, or to request or put in for something.
The definition of the word 'solicitation' means a process whereby one use to seek to obtain something by persuasion, a petition, formal application, request or entreaty.
The word that means a request to participate in something is, an invitation or an invite.
Request.
A person who puts in a formal request is often referred to as a petitioner or a claimant, depending on the context of the request.
Formal.
In the context of a formal meeting, an 'apology' refers to prior request to be absent from a meeting. It simply means, that the members are aware of your absence.
Resolution or a statement
Abdictation
spouse
Be careful... you might get a formal answer from him.
Inquiry