Lower Bounds on the Growth of Grigorchuk's Torsion Group

Details Lower Bounds on the Growth of Grigorchuk's Torsion Group Lower Bounds on the Growth of Grigorchuk's Torsion Group

1999-10-13

arxiv.org/abs/math/9910068v1

Internat. Math. Res. Notices 1998, no. 20, 1049--1054

Mathematics

Group Theory

Scientific paper

10.1155/S1073792898000622

In 1980 Rostislav Grigorchuk constructed a group $G$ of intermediate growth, and later obtained the following estimates on its growth $\gamma$: $e^{\sqrt{n}}\precsim\gamma(n)\precsim e^{n^\beta},$ where $\beta=\log_{32}(31)\approx0.991$. He conjectured that the lower bound is actually tight. In this paper we improve the lower bound to $e^{n^\alpha}\precsim\gamma(n),$ where $\alpha\approx0.5157$, with the aid of a computer. This disproves the conjecture that the lower bound be tight.

Affiliated with

Also associated with

No associations

Rating

Lower Bounds on the Growth of Grigorchuk's Torsion Group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lower Bounds on the Growth of Grigorchuk's Torsion Group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lower Bounds on the Growth of Grigorchuk's Torsion Group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675258