Right orderable residually finite p-groups and a Kourovka notebook problem
Group Theory
2007-05-23 v1
Abstract
A. H. Rhemtulla proved that if a group is a residually finite p-group for infinitely many primes p, then it is two-sided orderable. In problem 10.30 of the Kourovka notebook 14th. edition, N. Ya. Medvedev asked if there is a non-right-orderable group which is a residually finite p-group for at least two different primes p. Using a result of Dave Witte, we will show that many subgroups of finite index in GL_3(Z) give examples of such groups. On the other hand we will show that no such example can exist among solvable by finite groups.
Keywords
Cite
@article{arxiv.math/0107094,
title = {Right orderable residually finite p-groups and a Kourovka notebook problem},
author = {Peter A. Linnell},
journal= {arXiv preprint arXiv:math/0107094},
year = {2007}
}
Comments
2 pages, to appear in J. Algebra