Related papers: A note on torsion length
A finitely generated solvable group with unbounded iterated identity is constructed.
We classify finitely generated, residually finite automorphism-induced HNN-extensions in terms of the residual separability of a single associated subgroup. This classification provides a method to construct automorphism-induced…
We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented…
We investigate which free constructions (amalgamated products and HNN-extensions) over word hyperbolic groups produce groups that are again word hyperbolic. A complete answer is obtained for the case when the amalgamated subgroups are…
We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate…
All groups have 2 generators. For every prime power q, the Generalized Burnside Theorem (Theorem GB) produces an infinite number of solvable groups, Some, such as groups of a prime power exponent, have only elements of finite order and are…
The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free non-cyclic subgroup are proved.
All groups are 2-generator. For any prime-power q, Theorem 1 constructs a solvable matrix group over a quotient of a Laurent polynomial ring. This group is closely related to a group of exponent q as shown in Theorems 2 & 3 . Theorem 4 in…
We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first…
We show that the universal theory of torsion groups is strongly contained in the universal theory of finite groups. This answers a question of Dyson. We also prove that the universal theory of some natural classes of torsion groups is…
We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.
We find all the possible torsion groups of $\Q$-curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.
We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We…
This paper aims to investigate the self-similarity property in finitely-generated torsion-free nilpotent groups. We establish connections between geometric equivalence and self-similarity in these groups. Moreover, we show that any…
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying…
We show that every Coxeter group that is not virtually abelian and for which all labels in the corresponding Coxeter graph are powers of 2 or infinity can be mapped onto uncountably many infinite 2-groups which, in addition, may be chosen…
This is an expository article about groups generated by two isometries of the complex hyperbolic plane.
We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising…
In our previous paper, we introduced a hyperbolic jigsaw construction and constructed infinitely many non-commensurable, non-uniform, non-arithmetic lattices of $\mathrm{PSL}(2, \mathbb{R})$ with cusp set $\mathbb{Q} \cup \{\infty\}$…