Geodesic
Universal-existential equivalence of linear groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 205-212.

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In this paper, we prove that the groups $\mathrm{GL}$ and $\mathrm{SL}$ over infinite fields of characteristics not equal to $2$ are $(\forall \exists)$-equivalent if and only if their dimensions coincide and the corresponding fields are $(\forall \exists)$-equivalent. 
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P. Pritup. Universal-existential equivalence of linear groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 205-212. http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a10/

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