Related papers: Turn graphs and extremal surfaces in free groups
In this version small mistakes are corrected and the exposition is changed as suggested by the referee (to appear in Canadian Journal of Mathematics). The first main result of the paper is a criterion for a partially commutative group $\GG$…
Let Gamma be a connected, locally finite graph of finite tree width and G be a group acting on it with finitely many orbits and finite node stabilizers. We provide an elementary and direct construction of a tree T on which G acts with…
In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…
We give an alternative description of the top algebra of the free crossed square of algebras on 2-construction data in terms of tensors and coproducts of crossed modules of commutative algebras.
In this paper I consider the structure of the polylinear mapping of the free algebra over the commutative ring.
We prove a dichotomy between rationality and a natural boundary for the analytic behavior of the Reidemeister zeta function for automorphisms of non-finitely generated torsion abelian groups and for endomorphisms of groups $\mathbb Z_p^d,$…
We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.
The purpose of this paper is to extend some useful results, such as the multiplication being open, previously known for suitable finitely generated relatively free profinite semigroups, to relatively free profinite semigroupoids over…
We give a new geometric proof of a theorem of Heuer showing that, in the presence of letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups), and in particular in RAAGs, there is a sharp lower…
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge lengths on the sphere resulting in a flexible object. Our…
We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of…
We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering…
J.H.C. Whitehead's second free-group algorithm determines whether or not two given elements of a free group lie in the same orbit of the automorphism group of the free group. The algorithm involves certain connected graphs, and Whitehead…
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of rational subsets of groups, with particular emphasis on the automata-theoretic approach to finitely generated subgroups of free groups. Indeed, Stallings'…
We prove that the subgroup graph of a finite group $G$ is regular if and only if $G$ is cyclic with square-free order.
It is shown that there exist finitely generated infinite simple groups of infinite commutator width and infinite square width on which there exists no stably unbounded conjugation-invariant norm, and in particular stable commutator length…
A coarse group is a group endowed with a coarse structure so that the group multiplication and inversion are coarse mappings. Let $(X, \mathcal{E})$ be a coarse space and let $\mathfrak{M}$ be a variety of groups different from the variety…
We compute the rational stable homology of the automorphism groups of free nilpotent groups. These groups interpolate between the general linear groups over the ring of integers and the automorphism groups of free groups, and we employ…
This is a survey on (lack of) stable rationality over arbitrary fields (including algebraically closed fields). Topics addressed include: Rationality and unirationality, R-equivalence on rational points, Chow groups of zero-cycles, Galois…
We show that every word hyperbolic, surface-by-(noncyclic) free group Gamma is as rigid as possible: the quasi-isometry group of Gamma equals the abstract commensurator group Comm(Gamma), which in turn contains Gamma as a finite index…