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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2017, Volume 51, Issue 3, Pages 217–223
(Mi uzeru413)
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This article is cited in 2 scientific papers (total in 2 papers)
Mathematics
Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period $3$
V. S. Atabekyana, H. T. Aslanyanb, H. A. Grigorianb, A. E. Grigoryanb a Chair of Algebra and Geometry YSU, Armenia
b Chair of Mathematical Cybernetics RAU, Armenia
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 $\mathrm{Aut}(B(2,3)) \rightarrow GL_2(\mathbb{Z}_3)$ is the group of inner automorphisms of $B(2,3)$.
Received: 10.10.2017 Accepted: 20.10.2017
Citation:
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 YSU, Physical and Mathematical Sciences, 51:3 (2017), 217–223
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https://www.mathnet.ru/eng/uzeru413 https://www.mathnet.ru/eng/uzeru/v51/i3/p217
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Abstract page: | 219 | Full-text PDF : | 46 | References: | 30 |
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