Related papers: Transformation Digroups
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard…
In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…
A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…
We give two examples of categorical axioms asserting that a canonically defined natural transformation is invertible where the invertibility of any natural transformation implies that the canonical one is invertible. The first example is…
This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are…
We examine varieties of epigroups as unary semigroups, that is semigroups equipped with an additional unary operation of pseudoinversion. The article contains two main results. The first of them indicates a countably infinite family of…
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
In this note we introduce a notion of free cofibrations of permutative categories. We show that each cofibration of permutative categories is a retract of a free cofibration.
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
Various uses of the renormalization group are examined.
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.
Is the topological group of all motions (including translations) of an infinite-dimensional Hilbert space $H$ isomorphic to a subgroup of the unitary group $U(H)$? This question was asked by Su Gao. We answer the question in the…
We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.
In this paper, we focus on a question of M. Newman on isomorphic subgroups of solvable groups. We get a reduction theorem of this question: for each prime q, assume that this question holds for every characteristic q-groups, then this…
We describe the full automorphism group of the power (di)graph of a finite group. As an application, we solve a conjecture proposed by Doostabadi, Erfanian and Jafarzadeh in 2013.
The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…
We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…