English

The small index property for free nilpotent groups

Group Theory 2012-04-26 v2 Logic

Abstract

Let F be a relatively free algebra of infinite rank. We say that F has the SMALL INDEX PROPERTY if any subgroup of Gamma=Aut(F) of index at most rank(F) contains the pointwise stabilizer Gamma_(U) of a subset U of F of cardinality less than rank(F). We prove that every infinitely generated free nilpotent/abelian group has the small index property, and discuss a number of applications.

Keywords

Cite

@article{arxiv.1111.5635,
  title  = {The small index property for free nilpotent groups},
  author = {Vladimir Tolstykh},
  journal= {arXiv preprint arXiv:1111.5635},
  year   = {2012}
}

Comments

18 pp

R2 v1 2026-06-21T19:40:46.108Z