Related papers: 3-nets realizing a group in a projective plane

Let $n\geq 3,$ and let $Y$ be a simply connected, simple algebraic group of type $D_{n+1}$ over an algebraically closed field $K.$ Also let $X$ be the subgroup of type $B_n$ of $Y,$ embedded in the usual way. In this paper, we correct an…

We study the Prishchepov groups $P(r,n,k,s,q)$, a unifying family of cyclically presented groups that encompasses many classical cases. For $n$ coprime to $6$, we prove a conjecture essentially characterizing when these groups are perfect:…

On this paper we will present a construction of a CAT(0) cube complex (an infinite cube), on which the uncountable family of Grigorchuk groups $G_\omega$ act without bounded orbit. Moreover, if the sequence $\omega$ does not contain…

We study snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hagglund. We construct another infinite family, arising…

We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…

Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains…

A group $G$ is said to be $\frac{3}{2}$-generated if every nontrivial element belongs to a generating pair. It is easy to see that if $G$ has this property then every proper quotient of $G$ is cyclic. In this paper we prove that the…

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

It is known for a long time that a nonsingular real algebraic curve of degree 2k in the projective plane cannot have more than 7/2*k^2-9/4*k+3/2$ even ovals. We show here that this upper bound is asymptotically sharp, that is to say we…

We consider a family of finitely presented groups, called Universal Left Invertible Element (or ULIE) groups, that are universal for existence of one--sided invertible elements in a group ring K[G], where K is a field or a division ring. We…

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups…

We construct a family of PL triangulations of the $d$-dimensional real projective space $\mathbb{R}P^d$ on $\Theta((\frac{1+\sqrt{5}}{2})^{d+1})$ vertices for every $d\geq 1$. This improves a construction due to K\"{u}hnel on $2^{d+1}-1$…

We show that the family of nest algebras with $r$ non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local…

All varieties, extremal contractions, singularities are divided on exceptional and non-exceptional ones. Roughly speaking, there are the infinite families of non-exceptional varieties, extremal contractions or singularities and only the…

In this paper, we examine the combinatorial properties of conic arrangements in the complex projective plane that possess certain quasi-homogeneous singularities. First, we introduce a new tool that enables us to characterize the property…

We introduce the chain geometry $\Sigma(K,R)$ over a ring $R$ with a distinguished subfield $K$, thus extending the usual concept where $R$ has to be an algebra over $K$. A chain is uniquely determined by three of its points, if, and only…

Let $G$ be a group. Two elements $x,y \in G$ are said to be in the same $z$-class if their centralizers in $G$ are conjugate within $G$. Consider $\mathbb F$ a perfect field of characteristic $\neq 2$, which has a non-trivial Galois…

On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists, but not unique,…

For families of $K3$ surfaces, we establish a sufficient criterion for real or complex multiplication. Our criterion is arithmetic in nature. It may show, at first, that the generic fibre of the family has a nontrivial endomorphism field.…

We give here an explicit example of an algebraic family of foliations of CP^{2} which is topologically trivial but not analytically trivial. This example underlines the necessity of some assumptions in Y. Ilyashenko's rigidity theorem.