7 citations · 37 across the 19 of their papers we have counts for
23 papers
Invariant means, coset correct means and the Hahn-Banach Theorem
Armando Martino, Motiejus Valiunas
We show that, in ZF set theory, the existence of "coset correct means" on all groups is equivalent to the Hahn-Banach Theorem, as well as to the existence of invariant means on abe…
Outer automorphisms of HNN extensions of abelian groups
Naomi Andrew, Sam Hughes, Motiejus Valiunas
Let be a commensurating HNN extension of a finitely generated free abelian group. We characterise when is finitely generated and derive structural information…
Coset correct means on groups and the probability that two elements commute
Armando Martino, Motiejus Valiunas
Amenable groups are those admitting an invariant mean -- a finitely additive probability mean that assigns equal ``weight'' to any two translates of the same set. We introduce cose…
Moduli spaces of flat Riemannian metrics on orbifolds
Karla García, Ingrid Amaranta Membrillo Solis, Motiejus Valiunas
We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds , the Teichmüller space of flat metrics $…
Higher-rank GBS groups: non-positive curvature and biautomaticity
Sam Shepherd, Motiejus Valiunas
We characterise when a rank generalised Baumslag-Solitar group is CAT(0) and when it is biautomatic.
On the twisted conjugacy problem for large-type Artin groups
Martín Blufstein, Motiejus Valiunas
We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversi…
Free-by-cyclic groups are equationally Noetherian
Monika Kudlinska, Motiejus Valiunas
A group is said to be equationally Noetherian if every system of equations in is equivalent to a finite subsystem. We show that all free-by-cyclic groups are equationally N…
Right-angled Artin subgroups and free products in one-relator groups
Ashot Minasyan, Motiejus Valiunas
We investigate criteria ensuring that a one-relator group contains a right-angled Artin subgroup , corresponding to a finite graph . In particular, we prove that if $Γ…
A note on asynchronously automatic groups and notions of non-positive curvature
Sam Hughes, Motiejus Valiunas
We prove groups acting cocompactly on locally finite trees with hyperbolic vertex stabilisers are asynchronously automatic. Combining this with previous work of the authors, we obt…
Abelian subgroups of Helly groups
Motiejus Valiunas
We observe that abelian subgroups of Helly groups are finitely generated, and consequently, soluble subgroups of Helly groups are virtually abelian.
Basic Metric Geometry of the Bottleneck Distance
Mauricio Che, Fernando Galaz-García, Luis Guijarro +2
Given a metric pair , i.e. a metric space and a distinguished closed set , one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\…
Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity
Sam Hughes, Motiejus Valiunas
We construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives…
Commensurators of abelian subgroups of biautomatic groups
Motiejus Valiunas
We show that the commensurator of any finitely generated abelian subgroup in a biautomatic group centralises a finite-index subgroup of . We deduce that the CAT(0) groups in…
Helly groups, coarsely Helly groups, and relative hyperbolicity
Damian Osajda, Motiejus Valiunas
A simplicial graph is said to be (coarsely) Helly if any collection of pairwise intersecting balls has non-empty (coarse) intersection. (Coarsely) Helly groups are groups acting ge…
Isomorphism classification of Leary-Minasyan groups
Motiejus Valiunas
Recently, I. J. Leary and A. Minasyan studied the class of groups defined as commensurating HNN-extensions of . This class, containing the class of Baumslag-…
On equationally Noetherian and residually finite groups
Motiejus Valiunas
The aim of this paper is to compare and contrast the class of residually finite groups with the class of equationally Noetherian groups - groups over which every system of coeffici…
A note on growth of hyperbolic groups
Motiejus Valiunas
The following short note provides an alternative proof of a result of Coornaert: namely, that given a non-elementary word-hyperbolic group with a finite generating set , the…
Acylindrical hyperbolicity of groups acting on quasi-median graphs and equations in graph products
Motiejus Valiunas
In this paper we study group actions on quasi-median graphs, or 'CAT(0) prism complexes', generalising the notion of CAT(0) cube complexes. We consider hyperplanes in a quasi-media…
Negligibity of elliptic elements in ascending HNN-extensions of
Motiejus Valiunas
We study ascending HNN-extensions of finitely generated free abelian groups: examples of such include soluble Baumslag-Solitar groups and fundamental groups of orientable p…
Probabilistic nilpotence in infinite groups
Armando Martino, Matthew Tointon, Motiejus Valiunas +1
The 'degree of k-step nilpotence' of a finite group G is the proportion of the tuples (x_1,...,x_{k+1}) in G^{k+1} for which the simple commutator [x_1,...,x_{k+1}] is equal to the…
Negligibility of parabolic elements in relatively hyperbolic groups
Motiejus Valiunas
We study density of parabolic elements in a finitely generated relatively hyperbolic group with respect to a word metric. We prove this density to be zero (apart from degenerat…
Rational growth and degree of commutativity of graph products
Motiejus Valiunas
Let be an infinite group and let be a finite generating set for such that the growth series of with respect to is a rational function; in this case is said…
Orbits of crystallographic embedding of non-crystallographic groups and applications to virology
Reidun Twarock, Motiejus Valiunas, Emilio Zappa
The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with n…