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

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 $B(2,3)$. 
@article{UZERU_2017_51_3_a1,
     author = {V. S. Atabekyan and H. T. Aslanyan and H. A. Grigorian and A. E. Grigoryan},
     title = {Analogues of {Nielsen{\textquoteright}s} and {Magnus{\textquoteright}s} theorems for free {Burnside} groups of period $3$},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {217--223},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2017_51_3_a1/}
}
TY  - JOUR
AU  - V. S. Atabekyan
AU  - H. T. Aslanyan
AU  - H. A. Grigorian
AU  - A. E. Grigoryan
TI  - Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period $3$
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2017
SP  - 217
EP  - 223
VL  - 51
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2017_51_3_a1/
LA  - en
ID  - UZERU_2017_51_3_a1
ER  - 
%0 Journal Article
%A V. S. Atabekyan
%A H. T. Aslanyan
%A H. A. Grigorian
%A A. E. Grigoryan
%T Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period $3$
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2017
%P 217-223
%V 51
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2017_51_3_a1/
%G en
%F UZERU_2017_51_3_a1
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/