2017; Physical and Mathematical Sciences, 51(3 (244): 217–223
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ANALOGUES OF NIELSEN'S AND MAGNUS'S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3

Hayk Aslanyan*

Received: 2025-02-05 · Published: 2017-12-15

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CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ANALOGUES OF NIELSEN'S AND MAGNUS'S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3
Author
Hayk Aslanyan
Published
2017-12-15
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2017.51.3.217

Abstract

We prove that the free Burnside groups B(m,3) of period 3 and rank m≥1 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 Fm of rank m. We show that the kernel of the natural homomorphism Aut(B(2,3))→GL2(Z3) is the group of inner automorphisms of B(2,3).
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