Related papers: The Even Isomorphism Theorem for Coxeter Groups

We give an elementary proof of the group law for elliptic curves using explicit formulas.

We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Sch\"utzenberger, Gessel, and Roselle on various distributions of…

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of…

We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These theorems characterize ultragraphs for which the topological full group of an associated groupoid is an isomorphism invariant. These results extend…

We give formulas for the second and third integral homology of an arbitrary finitely generated Coxeter group, solely in terms of the corresponding Coxeter diagram. The first of these calculations refines a theorem of Howlett, while the…

We provide involutory symmetric generating sets of finitely generated Coxeter groups, fulfilling a suitable finiteness condition, which in particular is fulfilled in the finite, affine and compact hyperbolic cases.

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

We prove that affine Coxeter groups, even hyperbolic Coxeter groups and one-ended hyperbolic Coxeter groups are homogeneous in the sense of model theory. More generally, we prove that many (Gromov) hyperbolic groups generated by torsion…

We compute Aut(W) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in…

We prove the Horrocks theorem for unstable even-dimensional orthogonal Steinberg groups. The Horrocks theorem for Steinberg groups is one of the principal ingredients needed for the proof of the $\mathrm{K}_2$-analogue of Serre's problem,…

In this paper, we prove a fine condensation theorem. This is quite similar to condensation theorems for pure extender mice in the literature, except that condensation for iteration strategies has been added to the mix.

We provide the combinatorial proofs of the log-convexity for the derangement numbers in the symmetric group $\mathfrak{S}_n$, hyperoctahedral group $\mathfrak{B}_n$, and the demihyperoctahedral group $\mathfrak{D}_n$. We also show that the…

We prove an analogue of the Centralizer Theorem in the context of Artin-Tits groups.

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such…

In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.

In this work we give an explicit construction of the isomorphism of coefficient rings of Buchstaber and Krichever formal groups.

We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is…

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.

A solution of the isomorphism problem is presented for the class of Coxeter groups W that have a finite set of Coxeter generators S such that the underlying graph of the presentation diagram of the system (W,S) has the property that every…

Let $(W,S)$ be a Coxeter system and $\Gamma$ be a group of automorphisms of $W$ such that $\gamma(S)=S$ for all $\gamma \in \Gamma$. Then it is known that the group of fixed points $W^\Gamma$ is again a Coxeter group with a canonically…