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