Nikita Khrushchev:

A. was determined to follow in Stalin’s path, avoiding even the appearance of innovation.
B. was known as "old stone butt" by Western leaders.
C. was mocked as "Cottonman" by many Russians.
D. permitted the publication of One Day in the Life of Ivan Denisovich

Answer:A

To determine the correct answer, let's analyze each option and see which one aligns with the information about Nikita Khrushchev.

A. "Was determined to follow in Stalin's path, avoiding even the appearance of innovation."
This statement suggests that Khrushchev wanted to emulate Stalin and avoid innovation. However, this is not accurate. Khrushchev was known for implementing a series of reforms and denouncing some of Stalin's policies. Therefore, option A is incorrect.

B. "Was known as 'old stone butt' by Western leaders."
This option refers to a nickname attributed to Khrushchev by Western leaders. While Khrushchev did have confrontations with Western leaders, particularly during the Cold War, it is crucial to note that this option does not provide information relevant to the question. Hence, option B is not the correct answer either.

C. "Was mocked as 'Cottonman' by many Russians."
Similarly to option B, this statement refers to a nickname attributed to Khrushchev by some Russians. However, this has no relation to the publication of One Day in the Life of Ivan Denisovich. Therefore, option C is also incorrect.

D. "Permitted the publication of One Day in the Life of Ivan Denisovich."
This option pertains to the release of the book One Day in the Life of Ivan Denisovich. This work, authored by Aleksandr Solzhenitsyn, sheds light on the harsh conditions of Soviet prison camps under Stalin's regime. The fact that Khrushchev allowed its publication demonstrates a departure from Stalin's reign and his attempt at social and political reforms. Thus, option D is the correct answer.

In conclusion, the correct answer is D. Nikita Khrushchev permitted the publication of One Day in the Life of Ivan Denisovich.