One interesting experiment conducted with frog oocytes revealed that with an appropriate stimulus, the cyclic appearance and disappearance of cyclin occurs even in the absence of a nucleus. what does this result imply about the production of cyclin in oocytes during the cell cycle?

The production of cyclin in the absence of a nucleus means that the cyclin is being synthesized using pre-existing mRNA.

The absence of a nucleus means that the cell does not have its own DNA. DNA is transcribed on to mRNA molecules before the production of proteins. If a protein, such as cyclin in this case, is being synthesized without DNA, this means that the mRNA for the protein already exists in the cell.