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Gurleen Kaur

Publications and source records attributed to Gurleen Kaur.

13 recordsLinked to original sources
arXiv2026

On the representation dimension of finite $p$-groups

For a finite group $G$, the representation dimension $δ(G)$ is the least dimension of a faithful complex representation of $G$. We prove that $δ(H\times K) = δ(H) + δ(K)$ whenever $H$ and $K$ are $p$-groups for a fixed prime $p$, and show by example that this additivity can fail more generally for nilpotent groups. We also determine $δ(G)$ for several important classes of non-abelian $p$-groups, {\it viz.} VZ groups, Camina groups, and metacyclic groups; and compute $δ(G)$ for all groups of order $p^6$ ($p\geq 5$), organized by their isoclinism family.

math.GR↗
arXiv2026

Representation dimension of some finite groups

For a finite group $G$, the representation dimension is the smallest integer realizable as the degree of a complex faithful representation of $G$. In this article, we compute representation dimension for some $p$-groups, their direct products, and groups with certain conditions on nonlinear irreducible characters. We also make similar computations for the smallest integer realizable as the degree of an irreducible complex faithful representation of $G$, if one exists. In the appendix, we present GAP codes to compute these numbers.

math.GR↗
arXiv2025

Cyclic codes of length $n$ over finite chain rings

In this paper, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic group $G$ have been determined, and then the number of codewords and the minimum weight corresponding to a cyclic code have been computed.

math.RA↗
arXiv2025

EpiClim: Weekly District-Wise all-India multi-epidemics Climate-Health Dataset for accelerated GeoHealth research

Climate change significantly impacts public health, driving the emergence and spread of epidemics. Climate health models are essential for assessing and predicting disease outbreaks influenced by climatic variables like temperature and precipitation. For instance, dengue and malaria correlate with temperature changes, while cholera is linked to precipitation anomalies. Advances in AI-enabled weather prediction (AI-NWP) have improved forecasting, but integrating climate models with health systems is hindered by the lack of comprehensive, granular health datasets. This study introduces EpiClim: India's Epidemic-Climate Dataset, the first weekly district-wise dataset for major epidemics in India from 2009 to the present, sourced from the Integrated Disease Surveillance Programme (IDSP). The dataset, covering diseases like dengue, malaria, and acute-diarrheal disease, bridges the gap between climate and health data, enabling the integration of climate forecasts with epidemic prediction models. This work lays the foundation for coupling predictive climate health models with weather and climate models, advancing efforts to mitigate climate-induced public health crises.

physics.soc-ph↗
arXiv2025

Extended cut groups

A finite group G is said to be a cut group if all central units in the integral group ring ZG are trivial. In this article, we extend the notion of cut groups, by introducing extended cut groups. We study the properties of extended cut groups analogous to those known for cut groups and also characterise some substantial classes of groups having the property of being extended cut. A complete classification of extended cut split metacyclic groups has been presented.

math.GR↗
arXiv2024

Dynamics of Hot QCD Matter 2024 -- Hard Probes

The hot and dense QCD matter, known as the Quark-Gluon Plasma (QGP), is explored through heavy-ion collision experiments at the LHC and RHIC. Jets and heavy flavors, produced from the initial hard scattering, are used as hard probes to study the properties of the QGP. Recent experimental observations on jet quenching and heavy-flavor suppression have strengthened our understanding, allowing for fine-tuning of theoretical models in hard probes. The second conference, HOT QCD Matter 2024, was organized to bring the community together for discussions on key topics in the field. This article comprises 15 sections, each addressing various aspects of hard probes in relativistic heavy-ion collisions, offering a snapshot of current experimental observations and theoretical advancements. The article begins with a discussion on memory effects in the quantum evolution of quarkonia in the quark-gluon plasma, followed by an experimental review, new insights on jet quenching at RHIC and LHC, and concludes with a machine learning approach to heavy flavor production at the Large Hadron Collider.

nucl-ex↗
arXiv2024

On the Twisted Group Ring Isomorphism Problem for a class of groups

The twisted group ring isomorphism problem (TGRIP) is a variation of the classical group ring isomorphism problem. It asks whether the ring structure of the twisted group ring determines the group up to isomorphism. In this article, we study the TGRIP for direct product and central product of groups. We provide some criteria to answer the TGRIP for groups by answering the TGRIP for the associated quotients. As an application of these results, we provide several examples. Finally, we answer the TGRIP for extra-special p-groups, and for the groups of order $p^5$, where $p \geq 5$ is a prime, except a list of five groups.

math.GR↗
arXiv2023

On twisted group ring isomorphism problem for p-groups

In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently examined by Margolis-Schnabel. Our focus lies on a specific invariant, referred to as the generalized corank, which relates to the twisted complex group algebra isomorphism problem. We provide a solution for non-abelian $p$-groups with generalized corank at most three.

math.RA↗
arXiv2021

Central units of integral group rings of monomial groups

In this paper, it is proved that the group generated by Bass units contains a subgroup of finite index in the group of central units $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$ of the integral group ring $\mathbb{Z}G$ for a subgroup closed monomial group $G$ with the property that every cyclic subgroup of order not a divisor of $4$ or $6$ is subnormal in $G$. If $G$ is a generalized strongly monomial group, then it is shown that the group generated by generalized Bass units contains a subgroup of finite index in $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$. Furthermore, for a generalized strongly monomial group $G$, the rank of $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$ is determined. The formula so obtained is in terms of generalized strong Shoda pairs of $G$.

math.RA↗
arXiv2020

Connecting monomiality questions with the structure of rational group algebras

In recent times, there has been a lot of active research on monomial groups in two different directions. While group theorists are interested in the study of their normal subgroups and Hall subgroups, the interest of group ring theorists lie in the structure of their rational group algebras due to varied applications. The purpose of this paper is to bind the two threads together. Revisiting Dade's celebrated embedding theorem which states that a finite solvable group can be embedded inside some monomial group, it is proved here that the embedding is indeed done inside some generalized strongly monomial group. The so called generalized strongly monomial groups arose in a recent work of authors while understanding the algebraic structure of rational group algebras. Still unresolved monomiality questions have been correlated by proving that all the classes of monomial groups where they have been answered are generalized strongly monomial. The study also raises some intriguing questions weaker than those asked by Dornhoff and Isaacs in their investigations.

math.RA↗
arXiv2018

A generalization of strongly monomial groups

Olivieri, del R{\'ı}o and Sim{ó}n defined strongly monomial groups and a significant result proved by them is the explicit description of the simple components of the rational group algebra $\mathbb{Q}G$ of a strongly monomial group $G$. In this paper, generalized strongly monomial groups are defined, which is a generalization of strongly monomial groups. Beside strongly monomial groups, an extensive list of important families of groups which are generalized strongly monomial is produced. A description of the simple components of $\mathbb{Q}G$, when $G$ is a generalized strongly monomial group, is also provided. Furthermore, the work by Jespers, Olteanu, del R{\'ı}o and Van Gelder on the construction of a subgroup of finite index in the group of central units of integral group ring of a strongly monomial group has also been generalized.

math.RA↗
arXiv2017

Character triples and Shoda pairs

In this paper, a construction of Shoda pairs using character triples is given for a large class of monomial groups including abelian-by-supersolvable and subnormally monomial groups. The computation of primitive central idempotents and the structure of simple components of the rational group algebra for groups in this class are also discussed. The theory is illustrated with examples.

math.GR↗