S. Panja

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20242026

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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.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 $I ¨ $ is called rational if $I ¨ (g)$ is rational for all $g \in G$ . Also, a conjugacy class $x^{G}$ is called rational,…

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

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

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…