Related papers: z-Classes in Finite Coxeter Groups
We characterize when a finite lattice is distributive by the existences of some particular classes of Koszul filtrations.
We classify the semifields and division semirings containing the max-plus semifield $\mathbb{Z}_\mathrm{max}$, which are finitely generated as $\mathbb{Z}_\mathrm{max}$-semimodules.
In this paper we prove a series of matching theorems for two sets of Coxeter generators of a finitely generated Coxeter group that identify common features of the two sets of generators. As an application, we describe an algorithm for…
For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Carter and Orlik/Solomon. As a corollary we obtain an alternating…
We compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type.
In this paper we classify all capable finite $p$-groups with derived subgroup of order $p$ and $G/G'$ of rank $n-1$.
In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to…
In this short note we give a characterization of ZM-groups that uses the functions defined and studied in [3,4]. This leads to a proof of Conjecture 6 in [4].
We prove that affine Coxeter groups are profinitely rigid.
A finite group $G$ is called an F-group if for every $x, y \in G \setminus Z(G)$, $C(x) \leq C(y)$ implies that $C(x) = C(y)$. On the otherhand, two elements of a group are said to be $z$-equivalent or in the same $z$-class if their…
This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.
The purpose of this paper is to investigate the finite group which appears in the study of the Type II $\mathbf{Z}_4$-codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the…
Two elements in a group $G$ are said to $z$-equivalent or to be in the same $z$-class if their centralizers are conjugate in $G$. In \cite{kkj}, it was proved that a non-abelian $p$-group $G$ can have at most $\frac{p^k-1}{p-1} +1$ number…
I survey some recent developments in the theory of zeta functions associated to infinite groups and rings, specifically zeta functions enumerating subgroups and subrings of finite index or finite-dimensional complex representations.
We classify finite groups with a small average number of zeros in the character table.
In this paper we classify reflection subgroups of Euclidean Coxeter groups.
In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
In this paper we study affine reflection subgroups in arbitrary infinite Coxeter groups of finite rank. In particular, we study the distribution of roots of Coxeter groups in the root subsystems associated with affine reflection subgroups.…
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.
Eick & Leedham-Green sketched a construction for infinite sequences of finite $p$-groups with fixed coclass. These infinite sequences have turned out to be very useful in the theory of finite $p$-groups. We exhibit a detailed description…