Geodesic
Splitting Automorphisms of Order~$p^k$ of Free Burnside Groups are Inner
Matematičeskie zametki, Tome 95 (2014) no. 5, pp. 651-655.

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It is proved that, if the order of a splitting automorphism of odd period $n\ge 1003$ of a free Burnside group $B(m,n)$ is equal to a power of some prime, then the automorphism is inner. Thus, an affirmative answer is given to the question concerning the coincidence of the splitting automorphisms of the group $B(m,n)$ with the inner automorphisms for all automorphisms of order $p^k$ ($p$ is a prime). This question was posed in 1990 in “Kourovka Notebook” (see the 11th edition, Question 11.36.b).
Keywords: free Burnside group $B(m,n)$, splitting automorphism, inner automorphism. 
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V. S. Atabekyan. Splitting Automorphisms of Order~$p^k$ of Free Burnside Groups are Inner. Matematičeskie zametki, Tome 95 (2014) no. 5, pp. 651-655. http://geodesic.mathdoc.fr/item/MZM_2014_95_5_a1/

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