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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2014_95_5_a1,
     author = {V. S. Atabekyan},
     title = {Splitting {Automorphisms} of {Order~}$p^k$ of {Free} {Burnside} {Groups} are {Inner}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {651--655},
     publisher = {mathdoc},
     volume = {95},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_5_a1/}
}
TY  - JOUR
AU  - V. S. Atabekyan
TI  - Splitting Automorphisms of Order~$p^k$ of Free Burnside Groups are Inner
JO  - Matematičeskie zametki
PY  - 2014
SP  - 651
EP  - 655
VL  - 95
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_5_a1/
LA  - ru
ID  - MZM_2014_95_5_a1
ER  - 
%0 Journal Article
%A V. S. Atabekyan
%T Splitting Automorphisms of Order~$p^k$ of Free Burnside Groups are Inner
%J Matematičeskie zametki
%D 2014
%P 651-655
%V 95
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_5_a1/
%G ru
%F MZM_2014_95_5_a1
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/