Unique product groups and congruence subgroups

@article{Craig2020UniquePG,
  title={Unique product groups and congruence subgroups},
  author={William Craig and Peter A. Linnell},
  journal={arXiv: Group Theory},
  year={2020}
}
We prove that a uniform pro-p group with no nonabelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche-Wendt groups. 
Examples of non connective C*-algebras
Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, throughExpand
Properties of the combinatorial Hantzsche-Wendt groups
The combinatorial Hantzsche-Wendt group Gn = {x1, ..., xn | x −1 i x 2 jxix 2 j , ∀i 6= j} was defined by W. Craig and P. A. Linnell in [2]. For n = 2 it is a fundamental group of 3-dimensionalExpand

References

SHOWING 1-10 OF 25 REFERENCES
  • Doc. Math.
  • 2016
Analytic Pro P Groups
TLDR
The analytic pro p groups is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly. Expand
Rips–Segev torsion-free groups without the unique product property
Abstract We generalize the graphical small cancellation theory of Gromov to a graphical small cancellation theory over the free product. We extend Gromov's small cancellation theorem to the freeExpand
Finite index subgroups without unique product in graphical small cancellation groups
We construct torsion-free hyperbolic groups without unique product whose subgroups up to some given finite index are themselves non-unique product groups. This is achieved by generalising aExpand
On geometric aspects of diffuse groups
Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric point of view fromExpand
New examples of torsion-free non-unique product groups
Abstract. We give an infinite family of torsion-free groups that do not satisfy the unique product property. For these examples, we also show that each group contains arbitrarily large sets whoseExpand
Amenable groups with a locally invariant order are locally indicable
We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariantExpand
Commutator subgroups of Hantzsche–Wendt groups
Abstract A generalized Hantzsche–Wendt (GHW) group is by definition the fundamental group of a flat n-manifold with holonomy group ℤ2 n-1, and a Hantzsche–Wendt (HW) group is a GHW groupExpand
Congruence subgroups and the Atiyah conjecture
Let A denote the algebraic closure of the rationals Q in the complex numbers C. Suppose G is a torsion-free group which contains a congruence subgroup as a normal subgroup of finite index and denoteExpand
Profinite Groups
γ = c0 + c1p + c2p + · · · = (. . . c3c2c1c0)p, with ci ∈ Z, 0 ≤ ci ≤ p− 1, called the digits of γ. This ring has a topology given by a restriction of the product topology—we will see this below. TheExpand
...
1
2
3
...