Related papers: Characterization of Cyclically Fully commutative e…

We consider the group $\mathfrak{X}(G)$ obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from…

A group word $w$ is said to be strongly concise in a class $\mathcal{C}$ of profinite groups if, for every group $G$ in $\mathcal{C}$ such that $w$ takes less than $2^{\aleph_0}$ values in $G$, the verbal subgroup $w(G)$ is finite. Detomi,…

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…

A relation algebra is measurable if the identity element is a sum of atoms, and the square x;1;x of each subidentity atom x is a sum of non-zero functional elements. These functional elements form a group Gx. We prove that a measurable…

We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair, consisting of a group-like element and a character, in involution. This provides the key construct allowing to extend cyclic cohomology to Hopf…

The principal objects studied in this note are Coxeter groups $W$ that are neither finite nor affine. A well known result of de la Harpe asserts that such groups have exponential growth. We consider quotients of $W$ by its parabolic…

This paper contributes to the characterization of a certain class of commutative Hopf algebroids. It is shown that a commutative flat Hopf algebroid with a non zero base ring and a nonempty character groupoid is geometrically transitive if…

The problem whether a given permutation group contains a permutation with a given cycle type is studied. This problem is known to be NP-complete. In this paper it is shown that the problem can be solved in logspace for a cyclic permutation…

A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…

Suppose $C(G)$ denotes the set of all cyclic subgroups of a finite group $G$, and $\mathcal{O}_{2}(G)$ denotes the number of elements of order $2$ in $G$. In [Marius T., Finite groups with a certain number of cyclic subgroups. The American…

In [APS], the authors characterize the partitions of $n$ whose corresponding representations of $S_n$ have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups $W$. Namely, given a nontrivial…

Cycle sets are known to give non-degenerate unitary solutions of the Yang--Baxter equation and linear cycle sets are enriched versions of these algebraic systems. The paper explores the recently developed cohomology and extension theory for…

We define a new class of $\Xi$-coalescents characterized by a possibly infinite measure over the non negative integers. We call them symmetric coalescents since they are the unique family of exchangeable coalescents satisfying a symmetry…

The permutation groups of cyclic codes are widely applicable in determining the weight distribution of codes, decoding theory and various other areas. In this paper, by employing two distinct matrix representations, we can relate cyclic…

Let $W$ be a finite Coxeter group. We classify the reflection subgroups of $W$ up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup $R$ of $W$ the conjugacy class of its Coxeter…

Let $G$ be a finite group and let $c(G)$ be the number of cyclic subgroups of $G$. We study the function $\alpha(G) = c(G)/|G|$. We explore its basic properties and we point out a connection with the probability of commutation. For many…

A finite spin system invariant under a symmetry group G is a very illustrative example of the finite group action on a set of mappings f:X->Y. In the case of spin systems X is a set of spin carriers and Y contains 2s+1 z-components -s<=m<=s…

We extend the notion of proper elements to all Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to zero in the limit. This proves a conjecture of the third…

Let $(W, R)$ be a Coxeter system and let $w \in W$. We say that $u$ is a prefix of $w$ if there is a reduced expression for $u$ that can be extended to one for $w$. That is, $w = uv$ for some $v$ in $W$ such that $\ell(w) = \ell(u) +…

For every quiver (valued) of finite representation type we define a finitely presented group called a picture group. This group is very closely related to the cluster theory of the quiver. For example, positive expressions for the Coxeter…