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Chebyshevskii Sbornik, 2023, Volume 24, Issue 1, Pages 40–49
DOI: https://doi.org/10.22405/2226-8383-2023-24-1-40-49 (Mi cheb1281) 		 
The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable

V. G. Durneva, A. I. Zetkinaba

a Yaroslavl State University (Yaroslavl)
b Voroneg State University (Voroneg)
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DOI: https://doi.org/10.22405/2226-8383-2023-24-1-40-49
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 19-52-26006
Received: 09.01.2023
Accepted: 24.04.2023
Document Type: Article
UDC: 510.53, 512.54.05
Language: Russian
Citation: V. G. Durnev, A. I. Zetkina, “The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable”, Chebyshevskii Sb., 24:1 (2023), 40–49
Citation in format AMSBIB
\Bibitem{DurZet23}
\by V.~G.~Durnev, A.~I.~Zetkina
\paper The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable
\jour Chebyshevskii Sb.
\yr 2023
\vol 24
\issue 1
\pages 40--49
\mathnet{http://mi.mathnet.ru/cheb1281}
\crossref{https://doi.org/10.22405/2226-8383-2023-24-1-40-49}
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