GROUPS OF GIVEN INTERMEDIATE WORD GROWTH

被引：15

作者：

Bartholdi, Laurent ^{[1
]}

Erschler, Anna ^{[2
]}

机构：

[1] Univ Gottingen, Math Inst, D-37073 Gottingen, Germany

[2] Univ Paris 11, CNRS, Dept Math, F-91405 Orsay, France

来源：

ANNALES DE L INSTITUT FOURIER | 2014年 / 64卷 / 05期

关键词：

Growth of groups; self-similar groups; groups acting on trees; wreath products;

D O I：

10.5802/aif.2902

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that there exists a finitely generated group of growth similar to f for all functions f: R+-> R+ satisfying f (2R) <= f (R)(2) <= f (eta+R) for all R large enough and eta+ 2.4675 the positive root of X3 X2 2X 4. Set a_ = log2/ log ri+ 0.7674; then all functions that grow uniformly faster than exp(Ra) are realizable as the growth of a group. We also give a family of sum-contracting branched groups of growth exp(Ra) for a dense set of a E [a_, 1].

引用

页码：2003 / 2036

页数：34

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