Related papers: Cycle indices for the finite classical groups
In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their…
This article focuses on the study of the group of units of incidence rings, which is a class of infinite matrix groups indexed by ordered sets, on a topological perspective. We first show when these groups can inherit the topological…
A cyclic random walk is a random walk whose transition probabilities/rates can be written as a superposition of the empirical measures of a family of finite cycles. This identifies a convex set of models. We discuss the problem of…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a…
Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…
We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.
We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.
In this paper we introduce and study the concept of cyclic factorization number of a finite group G. By using the Mobius inversion formula and other methods involving the cyclic subgroup structure, this is explicitly computed for some…
This article investigates the traces of certain modules over rings of invariants associated with finite groups. More precisely, we provide a formula for computing the traces of arbitrary semi-invariants, thereby contributing to the…
Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
Any Schur ring is uniquely determined by a partition of the elements of the group. In this paper we present a general technique for enumerating Schur rings over cyclic groups using traditional Schur rings. We also survey recent efforts to…
The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.…
This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…
A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.
Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…
In this paper it is shown that every finite cyclic group satisfies the CI-property for the class of balanced configurations.
Latin squares have been historically used in order to create statistical designs in which, starting from a small number of experiments, it can be obtained a large experimental space. In this sense, the optimization of the selection of Latin…