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With countries there are certain conventions - federations/associations are usually given the definite article - The People's Republic of China, The Union of Socialist Soviet Republics, The United States of America. The European Union, The Malay States, The Ottoman Empire, The United Kingdom of Great Britain and Northern Ireland, The Netherlands.

Individual countries are almost always treated as proper names without an article. 

Official titles involving adjectives, however do - The Islamic Republic of Iran, The Republic of India , The Dominican Republic etc.

Island groups - again where the name is used adjectivally - often take 'The'. ie The Solomon Islands, The Virgin Islands, The Falklands, with individual islands as proper names eg South Georgia, Easter Island, Ascension Island etc.