Almost cyclic groups
Group Theory
2007-05-23 v1
Abstract
A group G is almost cyclic if there is an element x in G, such that for all g in G, there is an element y in G and an integer n with ygy^{-1} = x^n (that is, every element is conjugate to some power of x). W. Ziller asked whether there are finitely-presented almost cyclic groups which are not cyclic in connection with work on closed geodesics. V. Guba constructed an infinite (non-cyclic) finitely generated almost cyclic group. The principal results of this paper are: Solvable almost cyclic groups are cyclic, and one-relator almost cyclic groups are cyclic.
Cite
@article{arxiv.math/0511400,
title = {Almost cyclic groups},
author = {Bruce Ikenaga},
journal= {arXiv preprint arXiv:math/0511400},
year = {2007}
}