S. Panja

activity

20212026

most citedThe image of polynomials and Waring type problems on upper triangular matrix algebras

13 citations · 15 across the 26 of their papers we have counts for

collaborators

26 papers

math.RT2026

Wedderburn decomposition of the rational group algebras of $SL_{2} (q)$ and $PSL_{2} (q)$

Ram Karan Choudhary, Saikat Panja

In this article, we derive explicit combinatorial formulas, depending only on $q$ , for the Wedderburn decomposition of the rational group algebras of the finite linear groups $\ope…

math.NT2026

Periodic Points of Power Maps in Finite Matrix Groups and Algebras

Saikat Panja

Consider the power map $x \mapsto x^{L}$ for a prime $L \neq = 2$ such that $L ∣ q - 1$ where $q$ is a power of a prime. We determine the periodic points under this map for $\operatorname{M}…

math.GR2026

Lifting solutions of polynomial equations on matrices over field to complete local principal ideal rings

Saikat Panja, Ayon Roy, Anupam Singh

Let $O$ be a complete local principal ideal ring with residue field $k$ of characteristic not $2$ and $f \in O [x_{1}, x_{2}, \dots, x_{m}]$ . Take $A\in…

math.DS2025

Dynamics of Word Maps on Groups and Polynomial Maps on Algebras

Saikat Panja

We introduce the notions of Fatou and Julia sets in the context of word maps on complex Lie groups and polynomial maps on finite-dimensional associative $C$ -algebras. For t…

math.GR2025

Power maps on General Linear groups over finite principal ideal local rings of length two

Saikat Panja, Ayon Roy, Anupam Singh

Word maps have been studied for matrix groups over a field. We initiate the study of problems related to word maps in the context of the group $GL_{n} (O_{2})$ , where…

math.GR2025

Rational conjugacy classes and rational characters for some finite simple groups

Dilpreet Kaur, Saikat Panja

If $G$ is a finite group, an irreducible complex-valued character $χ$ is called rational if $χ (g)$ is rational for all $g \in G$ . Also, a conjugacy class $x^{G}$ is called rational, i…

math.RA2025

Polynomial maps with constants on split octonion algebras

Saikat Panja, Prachi Saini, Anupam Singh

Let $O (F)$ be the split octonion algebra over an algebraically closed field $F$ . For positive integers $k_{1}, k_{2} \geq 2$ , we study surjectivity of the map…

math.GR2024

A survey on power maps in groups

Saikat Panja, Anupam Singh

The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; $v i z .$ the map $x \mapsto x^{M}$ for a group $G$ ,…

math.GR2024

Word maps, polynomial maps and image ratios

Saikat Panja

If $A$ is a finite group (or a finite ring) and $ω$ is a word map (or a polynomial map), we define the quantity $∣ ω (A) ∣/∣ A ∣$ as the image ratio of $ω$ on $A$ and will be denoted by…

math.GR2024

Fibers of the square map in some finite groups of Lie type and an application

Saikat Panja

Let $G$ be one of the finite general linear, unitary, symplectic or orthogonal groups over finite fields of odd order. We find the cardinality of the fibers of the square map at a…

math.GR2024

Character covering number of $PSL_{2} (q)$

Namrata Arvind, Saikat Panja

For a group $G$ and a character $χ$ of $G$ , let $c (χ)$ denote the set of all irreducible characters of $G$ , occurring in $χ$ . We prove that whenever $q \geq 8$ , all non-trivial irre…

math.GR2024

Roots of identity in finite groups of Lie type

Saikat Panja

Given an integer $M \geq 2$ , we deploy the generating function techniques to compute the number of $M$ -th roots of identity in some of the well-known finite groups of Lie type, more…

math.GR2023

Images of polynomial maps with constants

Saikat Panja, Prachi Saini, Anupam Singh

Let $K$ be an algebraically closed field and $M (2, K)$ be the $2 \times 2$ matrix algebra over $K$ and $GL (2, K)$ be the invertible elements in $M (2, K)$ . We…

math.GR2023

Hopf Galois structures, skew braces for groups of size $p^{n} q$ : The cyclic Sylow subgroup case

Namrata Arvind, Saikat Panja

Let $n \geq 1$ be an integer, $p$ , $q$ be distinct odd primes. Let $G$ , $N$ be two groups of order $p^{n} q$ with their Sylow- $p$ -subgroups being cyclic. We enumerate the Hopf-Galois…

math.GR2023★ 1 cited

Surjectivity of polynomial maps on Matrices

Saikat Panja, Prachi Saini, Anupam Singh

For $n \geq 2$ , we consider the map on $M_{n} (K)$ given by evaluation of a polynomial $f (X_{1}, \dots, X_{m})$ over the field $K$ . In this article, we explore the image o…

math.GR2023

Powers in finite unitary groups

Saikat Panja, Anupam Singh

Let $U (n, F_{q^{2}})$ denote the subgroup of unitary matrices of the general linear group $GL (n, F_{q^{2}})$ which fixes a Hermitian form and $M \geq 2$ an…

math.GR2023

Cycle matrices: A combinatorial approach to the set-theoretic solutions of the Quantum Yang-Baxter Equation

Arpan Kanrar, Saikat Panja

An $n \times n$ matrix $M = [m_{ij}]$ with $m_{ij} \in U_{n} = {1, 2, \dots, n}$ will be called a cycle matrix if $(U_{n}, \cdot)$ is a cycle set, where $i \cdot j = m_{ij}$ . We study these matr…

math.CO2023

Independence complexes of wedge of graphs

Navnath Daundkar, Saikat Panja, Sachchidanand Prasad

In this article, we introduce the notion of a wedge of graphs and provide detailed computations for the independence complex of a wedge of path and cycle graphs. In particular, we…

math.GR2023

Acceptability of classical groups in non-zero characteristic

Saikat Panja

A group $G$ is called to be acceptable (due to M. Larsen) if for any finite group $H$ , two element-conjugate homomorphisms are globally conjugate. We answer the acceptability quest…

math.GM2022

Idempotents in integral ring of dihedral quandle

P Narayanan, Saikat Panja

We provide the structure of some idempotents in the integral ring of a dihedral quandles, for odd case. The solution is complete in case $n = 5$ . This produces an example of a connec…

math.RA2022★ 13 cited

The image of polynomials and Waring type problems on upper triangular matrix algebras

Saikat Panja, Sachchidanand Prasad

Let $p$ be a polynomial in non-commutative variables $x_{1}, x_{2}, \dots, x_{n}$ with constant term zero over an algebraically closed field $K$ . The object of study in this paper is the i…

math.GR2022

Counterexample to a conjecture about dihedral quandle

Saikat Panja, Sachchidanand Prasad

It was conjectured that the augmentation ideal of a dihedral quandle of even order $n > 2$ satisfies $∣ Δ^{k} (R_{n}) / Δ^{k + 1} (R_{n}) ∣ = n$ for all $k \geq 2$ . In this article we…

math.GR2022★ 1 cited

Powers in finite orthogonal and symplectic groups: A generating function approach

Saikat Panja, Anupam Singh

For an integer $M \geq 2$ and a finite group $G$ , an element $α \in G$ is called an $M$ -th power if it satisfies $A^{M} = α$ for some $A \in G$ . In this article, we will deal with the cas…

math.GR2022

Hopf-Galois Realizability of $Z_{n} ⋊ Z_{2}$

Namrata Arvind, Saikat Panja

Let $G$ and $N$ be finite groups of order $2 n$ where $n$ is odd. We say the pair $(G, N)$ is Hopf-Galois realizable if $G$ is a regular subgroup of $\h(N)=N\rtimes\au(N)$. In this a…

Wedderburn decomposition of the rational group algebras of SL2​(q) and PSL2​(q)

Periodic Points of Power Maps in Finite Matrix Groups and Algebras

Lifting solutions of polynomial equations on matrices over field to complete local principal ideal rings

Dynamics of Word Maps on Groups and Polynomial Maps on Algebras

Power maps on General Linear groups over finite principal ideal local rings of length two

Rational conjugacy classes and rational characters for some finite simple groups

Polynomial maps with constants on split octonion algebras

A survey on power maps in groups

Word maps, polynomial maps and image ratios

Fibers of the square map in some finite groups of Lie type and an application

Character covering number of PSL2​(q)

Roots of identity in finite groups of Lie type

Images of polynomial maps with constants

Hopf Galois structures, skew braces for groups of size pnq: The cyclic Sylow subgroup case

Surjectivity of polynomial maps on Matrices

Powers in finite unitary groups

Cycle matrices: A combinatorial approach to the set-theoretic solutions of the Quantum Yang-Baxter Equation

Independence complexes of wedge of graphs

Acceptability of classical groups in non-zero characteristic

Idempotents in integral ring of dihedral quandle

The image of polynomials and Waring type problems on upper triangular matrix algebras

Counterexample to a conjecture about dihedral quandle

Powers in finite orthogonal and symplectic groups: A generating function approach

Hopf-Galois Realizability of Zn​⋊Z2​

Wedderburn decomposition of the rational group algebras of $SL_{2} (q)$ and $PSL_{2} (q)$

Character covering number of $PSL_{2} (q)$

Hopf Galois structures, skew braces for groups of size $p^{n} q$ : The cyclic Sylow subgroup case

Hopf-Galois Realizability of $Z_{n} ⋊ Z_{2}$