Geodesic
An extension of a theorem of Neumann
Matematičeskie trudy, Tome 26 (2023) no. 1, pp. 41-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present article, we prove that every countable infinite group $G$ is embeddable into a countable infinite simple group $\overline{G}$ such that every equation of the form $$w(x_1,\dots,x_n)=g,$$ is solvable in $\overline{G}$, where $w$ is a nontrivial reduced group word in variables $x_1,\dots,x_n$, and $g\in G$. 
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V. G. Durnev; A. I. Zetkina. An extension of a theorem of Neumann. Matematičeskie trudy, Tome 26 (2023) no. 1, pp. 41-46. http://geodesic.mathdoc.fr/item/MT_2023_26_1_a2/

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[2] R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980

[3] V. Magnus, A. Karras, D. Soliter, Kombinatornaya teoriya grupp. Predstavlenie grupp v terminakh obrazuyuschikh i sootnosheii, Nauka, M., 1974

[4] B. H. Neumann, “Adjunction of elements to groups”, J. Lond. Math. Soc., 18 (1943), 4–11