Complex sentence: They were accused of selling the United States' top secret plans for building a nuclear bomb to the Soviet Union; at that time the United States was the sole country in the world with the knowledge and resources to build nuclear bombs.
Split into simpler sentences: They were accused of selling the United States' top secret plans for building a nuclear bomb to the Soviet Union. At the time, the United States was the sole country in the world with the knowledge and resources to build nuclear bombs.