Final answer:
The Nationalists led by Chiang Kai-shek retreated to Taiwan after being defeated by the Communists under Mao Zedong in 1949, where they continued the ROC. The U.S. and other Western nations initially supported the ROC in Taiwan as the legitimate government of China due to Cold War politics.
Step-by-step explanation:
The group that fled to Taiwan after being defeated by the Communists were the Nationalists, led by Chiang Kai-shek. Following the end of Japanese occupation of Taiwan at the close of World War II, the civil war between the Nationalists and the Communists in China resumed. Ultimately, in 1949 after suffering defeat by Mao Zedong's Communist forces, Chiang Kai-shek and the Nationalist Party retreated to Taiwan. They established what they considered to be the continuation of the Republic of China (ROC) there, in contrast to the People's Republic of China (PRC) declared by Mao on the mainland.
The United States and other Western powers initially refused to recognize the PRC, viewing the ROC government in Taiwan as the legitimate representative of China in part due to the dynamics of the Cold War. Cold War politics influenced the United Nations' recognition of the ROC until 1971 when it transferred recognition to the PRC as the legitimate government of China.