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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)
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.
Received: 09.01.2023 Accepted: 24.04.2023
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
Linking options:
https://www.mathnet.ru/eng/cheb1281 https://www.mathnet.ru/eng/cheb/v24/i1/p40
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Abstract page: | 40 | Full-text PDF : | 10 | References: | 8 |
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