Related papers: The theorems on freedom for relatively free groups…
We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger…
In [BB] Benjamin Baumslag proved that being fully residually free is equivalent to being residually free and commutative transitive (CT). Gaglione and Spellman [GS] and Remeslennikov [Re] showed that this is also equivalent to being…
Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published…
A group $G$ possesses the Magnus property if for every two elements $u$, $v \in G$ with the same normal closure, $u$ is conjugate to $v$ or $v^{-1}$. O. Bogopolski and J. Howie proved independently that the fundamental groups of all closed…
The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were…
Over a field of characteristic zero, we prove that the Freiheitssatz holds for brace algebras, the word problem for the brace algebras with a single defining relation is decidable, two generated subalgebras of free brace algebras are free,…
We prove an analogue of the fixed-point theorem for the case of definably amenable groups.
In this paper, we give an affirmative answer to Yamada's Conjecture on free topological groups, which was posed in [K. Yamada, {\it Fr\'echet-Urysohn spaces in free topological groups}, Proc. Amer. Math. Soc., {\bf 130}(2002), 2461--2469.].
We prove the Freiheitssatz for the variety of generic Poisson algebras.
The object of this paper is to describe a simple method for proving that certain groups are residually torsion-free nilpotent, to describe some new parafree groups and to raise some new problems in honour of the memory of Wilhelm Magnus.
It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement…
The notion of free link is a generalized notion of virtual link. In the present paper we define the group of free braids, prove the Alexander theorem that all free links can be obtained as closures of free braids and prove a Markov theorem,…
We give a complete classification of finitely generated virtually free groups up to $\forall\exists$-elementary equivalence. As a corollary, we give an algorithm that takes as input two finite presentations of virtually free groups, and…
We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The first-one concerns the non-superstability of such groups in most cases, and the second-one concerns the…
We show that the theory of the free group -- and more generally the theory of any torsion-free hyperbolic group -- is $n$-ample for any $n\geq 1$. We give also an explicit description of the imaginary algebraic closure in free groups.
A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…
Magnus' Freiheitssatz states that if a group is defined by a presentation with $m$ generators and a single relator containing the last generating letter, then the first $m-1$ letters freely generate a free subgroup. We study an analogue of…
We offer a direct proof of an elementary result concerning cohomological periods. As a corollary we show that given a finitely generated stably free resolution of Z over a finite group, two of its modules are free.
We extend the characterization of context-free groups of Muller and Schupp in two ways. We first show that for a quasi-transitive inverse graph $\Gamma$, being quasi-isometric to a tree, or context-free (finitely many end-cones types), or…
This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.