Algebraic entropy of elementary amenable groups
群论
2007-05-23 v1
摘要
We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups.
引用
@article{arxiv.math/0404075,
title = {Algebraic entropy of elementary amenable groups},
author = {D. V. Osin},
journal= {arXiv preprint arXiv:math/0404075},
year = {2007}
}
备注
20 pages; to appear in Geom. Dedicata