$\widetilde{B_0}$-invariant of groups

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.

In this version, typographical errors have been corrected, ensuring clarity and precision. Additionally, a previously stated theorem has been modified to reflect updated information or insights. These changes enhance the overall accuracy and readability of the document