$\tilde{B_0}$-invariant of groups

TL;DR

This paper generalizes the Bogomolov multiplier for groups within various group varieties, providing new theoretical insights and results on this extended concept.

Contribution

It introduces a generalized version of the Bogomolov multiplier applicable to different group varieties, expanding the scope of previous definitions.

Findings

New results on the generalized Bogomolov multiplier

Extension of the concept to various group varieties

Theoretical framework for further research

Abstract

The Bogomolov multiplier of a group $G$ introduced by Bogomolov in $1988$. After that in $2012$, Moravec introduced an equivalent definition of the Bogomolov multiplier. In this paper we generalized the Bogomolov multiplier with respect to a variety of groups. Then we give some new results on this topic.