English

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.

Keywords

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

R2 v1 2026-06-21T09:39:57.868Z