On the structure of groups defined by Kim and Manturov

TL;DR

This paper investigates the algebraic structure of groups introduced by Kim and Manturov, revealing they are finite, 2-step nilpotent 2-groups for all n ≥ 6, thus advancing understanding of their properties.

Contribution

It establishes that the groups Γₙ⁴ are finite and 2-step nilpotent 2-groups for all n ≥ 6, providing new structural insights.

Findings

Groups are finite for all n ≥ 6

They are 2-step nilpotent 2-groups

Structural properties are characterized for the first time

Abstract

We study the structure of a series of groups $\Gamma_n^4$ defined by Kim and Manturov. We show that the groups are finite for all $n \ge 6$ and in fact they are 2-step nilpotent $2$-groups.