Geodesic
An extension of a theorem of Neumann
Matematičeskie trudy, Tome 26 (2023) no. 1, pp. 41-46

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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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     author = {V. G. Durnev and A. I. Zetkina},
     title = {An extension of a theorem of {Neumann}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {41--46},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2023_26_1_a2/}
}
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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/