# Class 2 nilpotent and twisted Heisenberg groups

Every finitely generated nilpotent group $G$ of class at most $2$ can be obtained from $2$-generated such groups using central and subdirect products. As a corollary, $G$ embeds to a generalisation of the $3\times 3$ Heisenberg matrix group with entries coming from suitable abelian groups depending on $G$. In this talk, we present the key ideas of these statements and briefly mention how they emerged from investigating the so-called Jordan property of various transformation groups.

This talk is part of the Algebra Seminar series.