Related papers: Cut Groups: The Progress And The Problems
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…
We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.
We introduce a class of automorphisms of compact quantum groups which may be thought of as inner automorphisms and explore the behaviour of normal subgroups of compact quantum groups under these automorphisms. We also define the notion of…
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…
'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…
This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…
This article deals with the study of cactus groups from a combinatorial point of view. These groups have been gaining prominence lately in various domains of mathematics, amongst which are their relations with well-known groups such as…
In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions.…
We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of point sets which are obtained by a cut and projection scheme…
In \cite[Problem 72]{Fuchs60} Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In a…
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…
Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is…
The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$.…
We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…
This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key…
This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
In this paper we establish results that will be required for the study of the algebraic geometry of partially-commutative groups. We define classes of groups axiomatised by sentences determined by a graph. Among the classes which arise this…
It is well-known that any compact Lie group appears as closed subgroup of a unitary group, $G\subset U_N$. The unitary group $U_N$ has a free analogue $U_N^+$, and the study of the closed quantum subgroups $G\subset U_N^+$ is a problem of…