A finiteness condition on centralizers in locally nilpotent groups
Group Theory
2016-01-14 v1
Abstract
We give a detailed description of infinite locally nilpotent groups G such that the index |C_G (x) : <x>| is finite, for every non-normal cyclic subgroup <x> of G. We are also able to extend our analysis to all non-periodic groups satisfying a variation of our condition, where the requirement of finiteness is replaced with a bound.
Cite
@article{arxiv.1510.08251,
title = {A finiteness condition on centralizers in locally nilpotent groups},
author = {Gustavo A. Fernandez-Alcober and Leire Legarreta and Antonio Tortora and Maria Tota},
journal= {arXiv preprint arXiv:1510.08251},
year = {2016}
}
Comments
10 pages, submitted to an international journal. arXiv admin note: substantial text overlap with arXiv:1412.7330