Related papers: On Parallel Lines and Free Group

We prove that the palindromic width of HNN extension of a group by proper associated subgroups is infinite. We also prove that the palindromic width of the amalgamated free product of two groups via a proper subgroup is infinite (except…

A conjugation-free geometric presentation of a fundamental group is a presentation with the natural topological generators $x_1, ..., x_n$ and the cyclic relations: $x_{i_k}x_{i_{k-1}} ... x_{i_1} = x_{i_{k-1}} ... x_{i_1} x_{i_k} = ... =…

We show that if $N$, an open connected $n$-manifold with finitely generated fundamental group, is $C^{2}$ foliated by closed planes, then $\pi_{1}(N)$ is a free group. This implies that if $\pi_{1}(N)$ has an Abelian subgroup of rank…

We provide an alternative proof that the finite rational linear combination of radicals, under certain constraint, are linearly independent over $\mathbb{Q}$.

In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description for those of classes 2 and 3 is given. Furthermore, it is…

Our purpose is to visualize the pronilpotent completion of a finitely generated free group as a certain subgroup in the free Lie group.

In this note we prove a decomposition related to the affine fundamental group and the projective fundamental group of a line arrangement and a reducible curve with a line component. We give some applications to this result.

In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

It is proved that generalized free product of two finite p-groups is a conjugacy p-separable group if and only if it is residually finite p-groups. This result is then applied to establish some sufficient conditions for conjugacy…

This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative…

In this article we prove in the main theorem that, there is a bijection between the isomorphism classes of a certain type of real hyperplane arrangements on the one hand, and the antipodal pairs of convex cones of an associated…

In the category of free arrangements, inductively and recursively free arrangements are important. In particular, in the former, the conjecture by Terao asserting that freeness depends only on combinatorics holds true. A long standing…

We show that, for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal…

Generalizing a result of Yoshinaga in dimension 3, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced…

We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed the number of generators.

It is proved that there are triangle-free intersection graphs of line segments in the plane with arbitrarily small ratio between the maximum size of an independent set and the total number of vertices.

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.

We provide an algorithm that, given a finite set of generators for a subgroup $H$ of a finitely generated free group $F$, determines whether $H$ is echelon or not and, in case of affirmative answer, also computes a basis with respect to…

Recently, Cuntz and K\"uhne introduced a particular class of hyperplane arrangements stemming from a given graph $G$, so called connected subgraph arrangements $A_G$. In this note we strengthen some of the result from their work and prove…