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

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Showing 2023Show all

7 papers · 1 filter

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…

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

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