Anupam Singh

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20232026

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math.GR2026

Surjectivity of Engel Maps over trace zero matrices in $M_{2} (O)$

Ayon Roy, Anupam Singh

The surjectivity of various noncommutative polynomials has been studied extensively on Lie algebras over fields of different characteristics. In this article, we study the surjecti…

math.GR2026

Surjectivity of Engel Words on $SL_{2} (O)$ and $PSL_{2} (O_{2})$

Ayon Roy, Anupam Singh

The study of word maps and Waring-like problems has been widely pursued for finite simple groups, algebraic groups, and Lie groups. In this article, we study Engel word maps $e_{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.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.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.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…

Surjectivity of Engel Maps over trace zero matrices in M2​(O)

Surjectivity of Engel Words on SL2​(O) and PSL2​(O2​)

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

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

A survey on power maps in groups

Images of polynomial maps with constants

Surjectivity of Engel Maps over trace zero matrices in $M_{2} (O)$

Surjectivity of Engel Words on $SL_{2} (O)$ and $PSL_{2} (O_{2})$