Related papers: The integer group determinants for $Q_{16}$
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
This research is aimed to give a determinantal definition for the $q$-Appell polynomials and show some classical properties as well as find some interesting properties of the mentioned polynomials in the light of the new definition.
We study the average order of the divisor function, as it ranges over the values of binary quartic forms that are reducible over the rationals.
Quotient grading classes are essential participants in the computation of the intrinsic fundamental group $\pi_1(A)$ of an algebra $A$. In order to study quotient gradings of a finite-dimensional semisimple complex algebra $A$ it is…
An integral of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. In this paper, we prove that the integrability of a finite group is a decidable problem.
The structure of the unitary unit group of the group algebra ${\F}_{2^k} Q_{8}$ is described as a Hamiltonian group.
We solve Olga Taussky-Todd's circulant problem in the case of order 16.
In this paper, we continue the enumeration of Schur rings over cyclic groups. Cyclic groups of semiprime order $pq$, where $p$ and $q$ are distinct primes, are considered. Additionally, cyclic groups of order $4p$ are considered.
Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over the composite K of n quadratic number fields. Also, in Section 6, we obtain a characterization of…
We show that the Gromov-Lawson-Rosenberg conjecture for the Semi-Dihedral group of order 16 is true.
This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.
We prove that quadratical quasigroups form a variety Q of right and left simple groupoids. New examples of quadratical quasigroups of orders 25 and 29 are given. The fine structure of quadratical quasigroups and inter-relationships between…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.
We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit…
This document is rather a course about groups than a research paper. However, it can be of interest for many master students in mathematics which are devoted to the p-group classification theory. This paper is inspirated of the course of…
Recently, a construction of group divisible designs (GDDs) derived from the decoding of quadratic residue (QR) codes was given. In this paper, we extend the idea to obtain a new family of GDDs, which is also involved with a well-known…
Given commuting elements a, b of a group G and a group epimorphism q : G' \to G with finite kernel, the set of commuting lifts of a, b to G' is finite (possibly, empty). The second named author obtained a formula for the number of such…
In the manuscript [v4], we prove the uniqueness of a generalized quadrangle of order (4,16).
{\small In this paper we define and we study properties of} $\left(l,1,p+2q,q\cdot l\right) -$ {\small numbers,} $\left(l,1,p+2q,q\cdot l\right) -$ {\small quaternions,} $\left(l,1,p+2q,q\cdot l\right) -$ {\small symbol elements. Finally,…