One Question of the Theory of Numbered Groups

We show that the kernel of every numbered group is a permutation computable equivalence. We also prove the existence of a permutation computable equivalence over which no group is definable.

Authors

N. Kh. Kasymov (ORCID: https://orcid.org/0000-0003-4940-0649)

Institutions

National University of Uzbekistan (UZ)

Publication Details

Journal: Siberian Mathematical Journal
Published: 2025-03-01
DOI: https://doi.org/10.1134/s0037446625020077
Primary Topic: Computability, Logic, AI Algorithms
Type: article
Field-Weighted Citation Impact: 0.00

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article

One Question of the Theory of Numbered Groups

N. Kh. Kasymov

Mar 1, 2025

Siberian Mathematical Journal

Computability, Logic, AI Algorithms

article

One Question of the Theory of Numbered Groups

N. Kh. Kasymov

March 1, 2025article en

Abstract

We show that the kernel of every numbered group is a permutation computable equivalence. We also prove the existence of a permutation computable equivalence over which no group is definable.

Siberian Mathematical JournalVol. 66(2)

National University of Uzbekistan (UZ)

Reduced inequalities

Openalex Percentile: Top 94%

Computability, Logic, AI Algorithms

DOI Source OpenAlex

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One Question of the Theory of Numbered Groups — N. Kh. Kasymov · Siberian Mathematical Journal (2025) | TGRS Research Map | TGRS