Complex sentence: The Soviet program for producing a new generation of chess masters, originated and supervised by Nikolai Krylenko from the early 1930s, clearly was paying dividends, and from 1945 onwards, Soviet stars would dominate international chess for most of the rest of the 20th century.
Split into simpler sentences: The Soviet program for producing a new generation of chess masters, originated and supervised by Nikolai Krylenko from the early 1930s, clearly was paying dividends. From 1945 onwards, Soviet stars would dominate international chess for most of the rest of the 20th century.