Related papers: All finitely presented groups are QSF
This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.
This is the second of a Series of three papers, the first one published in Geom Dedicata 167 p. 91-121 (2013), proving that all finitely presented groups are QSF.
In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.
We define a `nice representation' of a finitely presented group G as being a non-degenerate essentially surjective simplicial map f from a `nice' space X into a 3-complex associated to a presentation of G, with a strong control over the…
It was recently proven by Esnault, Shusterman and the second named author, that the \'etale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend…
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups…
We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We prove that all Mathieu groups, some linear, and unitary groups are factorizable.
In this paper we prove that every finite group $G$ can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces $X$. Moreover, $X$ can be chosen to be the rationalization of an inflexible compact simply…
It is known that every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. In this paper, we give another proof which improves the result of Korkmaz. In addition, Korkmaz defined the genus of a…
We show that every countable group embeds in a group of type $FP_2$.
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.
We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$. We produce partial results for abelian varieties over a general finite…
We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.
It is known that in any free group the isolator of finitely generated subgroup is finitely generated subgroup. A very simple proof of this statement is proposed.
We observe that the group of all lifts of elements of Thompson's group $T$ to the real line is finitely presented and contains the additive group $\mathbb{Q}$ of the rational numbers. This gives an explicit realization of the Higman…
We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…