Geodesic
Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period $3$
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 3, pp. 217-223 
V. S. Atabekyan; H. T. Aslanyan; H. A. Grigorian; A. E. Grigoryan. Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period $3$. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 3, pp. 217-223. http://geodesic.mathdoc.fr/item/UZERU_2017_51_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the free Burnside groups $B(m,3)$ of period 3 and rank $m\geq1$ have Magnus's property, that is if in $B(m,3)$ the normal closures of $r$ and $s$ coincide, then $r$ is conjugate to $s$ or $s^{-1}$. We also prove that any automorphism of $B(m,3)$ induced by a Nielsen automorphism of the free group $F_m$ of rank $m$. We show that the kernel of the natural homomorphism $\mathrm{Aut}(B(2,3)) \rightarrow GL_2(\mathbb{Z}_3)$ is the group of inner automorphisms of $B(2,3)$.

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