Final answer:
The Drosophila-specific DNA-based (Class II) transposon is known as the P element, which is an autonomous element encoding its own transposase, allowing it to mobilize independently.
Step-by-step explanation:
The name of a Drosophila-specific DNA-based (Class II) transposon is the P element. These elements are a type of transposon found in the fruit fly, Drosophila melanogaster, and are an example of a DNA-based transposon that moves through a cut-and-paste mechanism. Unlike the maize Ac/Ds system, where the Ac element provides the transposase enzyme that the Ds element lacks, P elements are autonomous since they encode their own transposase. This allows them to mobilize independently within the Drosophila genome.