Finitely generated groups with polynomial index growth
Group Theory
2012-03-07 v1
Abstract
We prove that a finitely generated soluble residually finite group has polynomial index growth if and only if it is a minimax group. We also show that if a finitely generated group with PIG is residually finite-soluble then it is a linear group. These results apply in particular to boundedly generated groups; they imply that every infinite BG residually finite group has an infinite linear quotient.
Cite
@article{arxiv.0711.0687,
title = {Finitely generated groups with polynomial index growth},
author = {Laszlo Pyber and Dan Segal},
journal= {arXiv preprint arXiv:0711.0687},
year = {2012}
}
Comments
To appear in Crelle's Journal