I'm not sure exactly what you're asking (possible language barrier?)
If you're looking for ways to integrate googleapps into filemaker, they (google) have an API that could make it possible to send and receive documents/objects between googleapps and filemaker
It's probably easiest to start with the REST API apps for google apps, which uses a URL based protocol to return JSON encoded data from google. FileMaker's Insert From URL script step is a great way to pull the data into FileMaker.
Without having specific goals though, the feedback you'll get here is limited.
Ah, I see this was posted in one of the Japanese forums but was in English. Sorry!