The Jupiter Mining Corporation or JMC was the section of the Space Corps that licensed ships, like Red Dwarf, to conduct mining operations throughout Earth's Solar System, and also interstellar, into Deep Space around the Galaxy.
The English language was the offical language of the Space Corps, but the Jupiter Mining Corporation also made extensive use of Esperanto. Many of the corridors of Red Dwarf are labelled in both English and Esperanto.
They made cut-backs before Red Dwarf left Earth for the last time, removing their Quark-level matter/anti-matter Engine Core and causing the ship to be laid out differently, including removing a Karaoke Bar on C deck. (RD: Back in the Red I)
The Jupiter Mining Corporation was a mining company that had an office at room 02-842 on the Promenade of Starbase Deep Space 9 in Star Trek: Deep Space Nine This establishment, which seems to be named after or originate from Jupiter, is listed on a Promenade directory map seen in many episodes of DS9. It is a deliberate reference to Red Dwarf.
The insignia of JMC takes heavy inspiration from the logo of the DeLorean Motor Company/DMC.