Groups of small period growth

On the Word and Period Growth of some Groups of Tree Automorphisms

We generalize a class of groups defined by Rostislav Grigorchuk to a much larger class of groups, and provide upper and lower bounds for their word growth (they are all of intermediate growth) and period growth (under a small additional condition, they are periodic).

Growth of periodic quotients of hyperbolic groups

Let G be a non-elementary torsion-free hyperbolic group. We prove that the exponential growth rate of the periodic quotient G/G^n tends to the one of G as n odd approaches infinity. Moreover we provide an estimate at which the convergence is taking place.

Palindromic subshifts and simple periodic groups of intermediate growth

We describe a new class of groups of Burnside type, giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.

周期增长与共上下文无关群

Period growth and co-context-free groups

本文研究了共上下文无关群中的周期增长，通过Thompson群和Houghton群等例子，提出了计算元素阶数和旋转数的高效算法，并给出了词度量的上界改进。

Growth rates of small cancellation groups

We estimate growth rates for small cancellation groups. In particular we show that there is a continuum possible values for exponential growth rates.

Growth of periodic Grigorchuk groups

On torsion Grigorchuk groups we construct random walks of finite entropy and power-law tail decay with non-trivial Poisson boundary. Such random walks provide near optimal volume lower estimates for these groups. In particular, for the first Grigorchuk group $G$ we show that its volume growth function $v_{G,S}(n)$ satisfies that $\lim_{n\to\infty}\log\log v_{G,S}(n)/\log n=α_{0}$, where $α_{0}=\frac{\log2}{\logλ_{0}}\approx0.7674$, $λ_{0}$ is the positive root of the polynomial $X^{3}-X^{2}-2X-4$.