ANALOGUES OF NIELSEN'S AND MAGNUS'S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3

Authors

  • V.S. Atabekyan Chair of Algebra and Geometry, YSU, Armenia
  • H.T. Aslanyan Chair of Mathematical Cybernetics, RAU, Armenia
  • H.A. Grigoryan Chair of Mathematical Cybernetics, RAU, Armenia
  • A.E. Grigoryan Chair of Mathematical Cybernetics, RAU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2017.51.3.217

Keywords:

Nielsen automorphism, Magnus’s property, tame automorphism, free Burnside group, free group

Abstract

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 $\text{Aut}(B(2,3)) \rightarrow GL_2(\mathbb{Z}_3)$ is the group of inner automorphisms of $B(2,3)$.

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Published

2017-12-15

How to Cite

Atabekyan, V., Aslanyan, H., Grigoryan, H., & Grigoryan, A. (2017). ANALOGUES OF NIELSEN’S AND MAGNUS’S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3. Proceedings of the YSU A: Physical and Mathematical Sciences, 51(3 (244), 217–223. https://doi.org/10.46991/PYSU:A/2017.51.3.217

Issue

Section

Mathematics