Multiplicative Lie algebra structure on nilpotent group of class $2$

TL;DR

This paper investigates the properties of multiplicative Lie algebra structures on nilpotent groups of class 2 and introduces a method for constructing such structures on specific group extensions.

Contribution

It provides a new approach to determine multiplicative Lie algebra structures on groups extending Lie rings, especially for metacyclic and class 2 nilpotent groups.

Findings

Characterization of multiplicative Lie algebra structures on class 2 nilpotent groups

A method for constructing these structures on group extensions

Application to metacyclic groups

Abstract

This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie ring by another Lie ring such as a metacyclic group and a nilpotent group of class $2$.