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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2019, Issue 2(39), Pages 54–60 (Mi pfmt637)  

MATHEMATICS

On the Tits alternative for generalized tetraedron groups of type $(2, 2, N, 2, 2, 2)$

V. V. Beniash-Kryvetsa, Y. A. Yushkevichb

a Belarusian State University, Minsk
b M. Tank Belarusian State Pedagogical University, Minsk
References:
Abstract: Generalized tetraedron groups have a presentation of the form
$$ \Gamma=\left\langle x_1,x_2,x_3\mid x_1^{k_1}=x_2^{k_2}=x_3^{k_3}=R_{12}(x_1,x_2)^l=R_{23}(x_2,x_3)^m=R_{13}(x_1,x_3)^n=1\right\rangle. $$
There exists a Rosenberger’s conjecture that the Tits alternative holds for generalized tetrahedron groups. This conjecture is open for groups of the form $\left\langle x_1,x_2,x_3\mid x_1^{k_1}=x_2^{k_2}=x_3^{k_3}=R_{12}(x_1,x_2)^2=(x_1^\alpha x_3^\beta)^2=(x_2^\gamma x_3^\delta)^2=1\right\rangle$, $\frac1{k_1}+\frac1{k_2}+\frac1{k_3}\geqslant\frac12$. In this paper, a number of sufficient conditions are found for fulfillment the Tits alternative for groups
$$ \Gamma=\left\langle a,b,c\mid a^2=b^n=c^2=R(a,b)^2=(b^\alpha c)^2=(ac)^2=1\right\rangle. $$
Keywords: generalized tetraedron group, Tits alternative, free group, almost solvavle group.
Received: 11.03.2019
Document Type: Article
UDC: 512.543
Language: Russian
Citation: V. V. Beniash-Kryvets, Y. A. Yushkevich, “On the Tits alternative for generalized tetraedron groups of type $(2, 2, N, 2, 2, 2)$”, PFMT, 2019, no. 2(39), 54–60
Citation in format AMSBIB
\Bibitem{BenYus19}
\by V.~V.~Beniash-Kryvets, Y.~A.~Yushkevich
\paper On the Tits alternative for generalized tetraedron groups of type $(2, 2, N, 2, 2, 2)$
\jour PFMT
\yr 2019
\issue 2(39)
\pages 54--60
\mathnet{http://mi.mathnet.ru/pfmt637}
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  • https://www.mathnet.ru/eng/pfmt/y2019/i2/p54
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    Проблемы физики, математики и техники
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