One question of the theory of numbered groups

N. Kh. Kasymov

Mirzo Ulugbek National University, Tashkent, Uzbekistan

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.

Keywords: numbered group, definability of a group over equivalence, permutation computable equivalence.

UDC: 510.5

MSC: 35R30

Received: 15.08.2024
Revised: 28.01.2025
Accepted: 25.02.2025

DOI: 10.33048/smzh.2025.66.207

 English version: Siberian Mathematical Journal, 2025, 66:2, 298–302