The option that best describes the demographic changes that occurred in Kazakhstan under the Soviet Union is:
Kazakhs became a minority group in Kazakhstan.
During the Soviet era, particularly during the 1930s to the 1980s, there was significant migration of non-Kazakh ethnic groups into Kazakhstan, such as Russians, Ukrainians, and Germans. This led to a decline in the proportion of Kazakhs, resulting in them becoming a minority in their own country.