13 problems

Let $G$ be an ordinary finitely generated group, and compare its standard growth with its conjugacy growth. Guba–Sapir conjecture. Exponential standard growth of $G$ implies expone…

Let $G$ be a finitely presented group, and let its conjugacy growth series be the formal power series whose coefficients are the values of the conjugacy growth function. Ciobanu–Ev…

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…

For a group $G=\langle X\rangle$, let $[g]_c$ denote the conjugacy class of $g\in G$, and define the length up to conjugacy by … The strict conjugacy growth function is…

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…

Rational conjugacy growth conjecture. The spherical conjugacy growth series of $G$ is rational only if $G$ is virtually abelian.

Let $G$ be a finitely generated group, and let the conjugacy growth series of $G$ be the generating series associated with the number of conjugacy classes intersecting the ball of…

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 generated virtually nilpotent group, and let conjugacy growth be viewed as a function associated to a finite generating set, up to the usual equivalence. Virt…

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…

Let $G$ be a finitely presented group and let $S$ be any finite generating set. The conjugacy growth rate conjecture. The conjugacy and standard growth rates of $G$ with respect to…

Let $G$ be an amenable group, and let its standard growth function be amma_G(n)=#B(n) and its conjugacy growth function be…