Geodesic
The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable
Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 40-49

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In paper proved that it is impossible to build an algorithm that allows you to determine from an arbitrary finite task of the group whether it is solvable her positive theory. The specified group property is not Markov, so the fundamental Adyan-Rabin theorem does not apply to it.
Keywords: positive formula, positive group theory, positive group class theory, algorithmic solvability, algorithmic insolubility. 
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     title = {The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable},
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V. G. Durnev; A. I. Zetkina. The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable. Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 40-49. http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a3/