6 problems

Let $G$ be a finitely presented group, and let $X$ be a finite generating set. The conjugacy growth series of $G$ with respect to $X$ is the generating function … where…

Let $G$ be a finitely presented group with a finite generating set $X$. Its conjugacy growth series is the generating function … where $c_{G,X}(n)$ counts the conjugacy classes hav…

Let $G$ be a finitely generated nilpotent group, and for each $i$ let $r_i$ be the torsion-free rank of the quotient $G^{(i+1)}/G^{(i)}$. Nilpotent conjugacy-growth rank conjecture…

Let $G$ be a finitely presented group that is not virtually abelian, and let its conjugacy growth series be the formal power series whose coefficients are the values of the conjuga…

Let $G$ be a finitely presented group that is not virtually abelian, and let a finite generating set mean any finite generating set of $G$. The general conjugacy-growth transcenden…

For an integer $k\geq 2$, let $BS(1,k)=\langle a,t\mid tat^{-1}=a^k\rangle$, and let a finite generating set mean any finite generating set of this group. The Baumslag–Solitar tran…