Related papers: Infinite presentability of groups and condensation
We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…
Let $ x $ be an element of a finite group $ G $ and denote the order of $ x $ by $ \mathrm{ord}(x) $. We consider a finite group $ G $ such that $ \gcd(\mathrm{ord}(x),\mathrm{ord}(y))\leqslant 2 $ for any two vanishing elements $ x $ and $…
We show that there exist non-unitarizable groups without non-abelian free subgroups. Both torsion and torsion free examples are constructed. As a by-product, we show that there exist finitely generated torsion groups with non-vanishing…
We construct the first examples of finitely presented simple groups of orientation-preserving homeomorphisms of the real line. Our examples are also of type $F_{\infty}$, have infinite geometric dimension, and admit a nontrivial homogeneous…
We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the…
The study of minimal complements in a group or a semigroup was initiated by Nathanson. The notion of minimal complements and being a minimal complement leads to the notion of co-minimal pairs which was considered in a prior work of the…
We introduce a formalism of infinite, linearly ordered products in general groups. Using this, we define infinite compositions in certain groups of formal power series such as transseries. We show that such groups can sometimes be…
We characterize the group property of being with infinite conjugacy classes (or icc, i.e. \not= 1 and of which all conjugacy classes except 1 are infinite) for finite extensions of group.
We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor…
A finite presentation for the subgroup of the mapping class group of a compact non-orientable surface generated by all Dehn twists was given by Stukow. In this paper, we give an infinite presentation for this group, mainly using the…
We prove finiteness properties for groups of homeomorphisms that have finitely many "singular points", and we describe the normal structure of such groups. As an application, we prove that every countable abelian group can be embedded into…
We find a condition on the acylindrical action of a finitely presented group on a simplicial tree which guarantees that this action will be dominated by an acylindrical action with finitely generated edge stabilisers, and find the first…
In the article \cite{BM1.22}, the minimum volume entropy is introduced for each group of finite presentation and there we study some of its general properties. Another concept of minimum volume entropy for geometrically finite groups has…
In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all "separating twists", all "bounding pair maps", and all "commutators of simply…
The question of whether or not all finitely presented groups are semistable at infinity has been studied for over 40 years. In 1986, we defined what it means for a finitely generated group to be semistable at infinity - in analogy with the…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
A result of D. Segal states that every complex irreducible representation of a finitely generated nilpotent group $G$ is monomial if and only if $G$ is abelian-by-finite. A conjecture of A. N. Parshin, recently proved affirmatively by I.V.…
We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.
We give an infinite presentation for the mapping class group of a non-orientable surface. The generating set consists of all Dehn twists and all crosscap pushing maps along simple loops.
We construct new classes of self-similar groups : S-aritmetic groups, affine groups and metabelian groups. Most of the soluble ones are finitely presented and of type FP_{n} for appropriate n.