相关论文: On irreducible n-ary quasigroups with reducible re…

We study the class of symmetric $n$-ary bands. These are $n$-ary semigroups $(X,F)$ such that $F$ is invariant under the action of permutations and idempotent, i.e., satisfies $F(x,\ldots,x)=x$ for all $x\in X$. We first provide a structure…

We prove the main result that a groupoid of order n is an idempotent k-translatable quasigroup if and only if its multiplication is given by x.y = (ax+by)(mod n), where a+b = 1(mod n), a+bk = 0(mod n) and (k,n)= 1. We describe the structure…

Let $G$ be a finite group and $p$ be a prime number dividing the order of $G$. An irreducible character $\chi$ of $G$ is called a quasi $p$-Steinberg character if $\chi(g)$ is nonzero for every $p$-regular element $g$ in $G$. In this paper,…

A permutation group is said to be quasiregular if every its transitive constituent is regular, and a quasiregular coherent configuration can be thought as a combinatorial analog of such a group: the transitive constituents are replaced by…

We investigate the multiplication group of a special class of quasigroup called AG-group. We prove some interesting results such as: the multiplication group of an AG-group of order n is non-abelian group of order 2n and its left section is…

Motivated by a problem from behavioral economics, we study subgroups of permutation groups that have a certain strong symmetry. Given a fixed permutation, consider the set of all permutations with disjoint inversion sets. The group is…

In this paper we present a graph theoretic construction of Steiner quadruple systems (SQS) admitting abelian groups as point-regular automorphism groups. The resulting SQS has an extra property which we call A-reversibility, where A is the…

An action of a group $G$ on a set $X$ is said to be quasi-n-transitive if the diagonal action of $G$ on $X^n$ has only finitely many orbits. We show that branch groups, a special class of groups of automorphisms of rooted trees, cannot act…

We consider the graphs whose edges are marked by the integers (weights) from $0$ to $q-1$ (zero corresponds to no-edge). Such graph is called additive if its vertices can be marked in such a way that the weight of every edge is equal to the…

An irreducible ordinary character of a finite reductive group is called quadratic unipotent if it corresponds under Jordan decomposition to a semisimple element $s$ in a dual group such that $s^2=1$. We prove that there is a bijection…

A subset $U$ of a set $S$ with a binary operation is called {\it avoidable} if $S$ can be partitioned into two subsets $A$ and $B$ such that no element of $U$ can be written as a product of two distinct elements of $A$ or as the product of…

For positive $q\neq1$, the $q$-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend…

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given…

Any Neumann quasigroup $(Q, \cdot)$ (quasigroup with Neumann identity $ x \cdot(yz \cdot yx) = z$ is called Neumann quasigroup) can be presented in the form $x\cdot y = x-y$, where $(Q, +)$ is an abelian group. Automorphism group of Neumann…

A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as a# b where a and b are elements of S and if, in addition, every element of S that is square…

We give a classification of all irreducible completely pointed $U_q(\mathfrak{sl}_{n+1})$ modules over a characteristic zero field in which $q$ is not a root of unity. This generalizes the classification result of Benkart, Britten and…

A subset of an abelian group is {\em sequenceable} if there is an ordering $(x_1, \ldots, x_k)$ of its elements such that the partial sums $(y_0, y_1, \ldots, y_k)$, given by $y_0 = 0$ and $y_i = \sum_{j=1}^i x_i$ for $1 \leq i \leq k$, are…

Let $\mathcal{PORD}_{n}$ be the semigroup consisting of all oriented and order-decreasing partial transformations on the finite chain $X_{n}=\{ 1<\cdots<n \}$. Let $\mathcal{IORD}_{n}$ be the subsemigroup of $\mathcal{PORD}_{n}$ consisting…

An irreducible character of a finite group $G$ is called quasi $p$-Steinberg character for a prime $p$ if it takes a nonzero value on every $p$-regular element of $G$. In this article, we classify the quasi $p$-Steinberg characters of…

Let $U(q)$ be a Sylow $p$-subgroup of the Chevalley groups $D_4(q)$ where $q$ is a power of a prime $p$. We describe a construction of all complex irreducible characters of $U(q)$ and obtain a classification of these irreducible characters…