The Apple Music's tracks has DRM (Digital Rights Management) protected, which not allow the subscribers won't just sign up the streaming service and then leave away with a bunch of songs downloaded for offline listening. If you want to download Apple Music to listening on MP3 player, iPod Nano and more devices, you need to remove DRM from Apple Music.
I search in Google to find a Apple Music DRM removal software, I find an Apple Music Converter, named UkeySoft Apple Music Converter, it really helps me remove DRM from Apple music, however, this UkeySoft is only for personal entertainment and it is not allowed for commercial use. So, UkeySoft is legally for those who want to use Apple Music for personal entertainment.
This UkeySoft app can decode DRM and convert songs into unencrypted format, such as MP3, M4A, FLAC etc. Unlocking DRM, converting music or audiobook, multi-device playback, ID3 tags editor are the main features of this amazing product.
For example, you can use UkeySoft Apple Music Converter to remove DRM from Apple Music and convert iTunes M4P files to MP3, and then transfer the songs to iPod Nano for offline listening.