Amit Kulshrestha

activity

20112026

most citedAsymptotics of the powers in finite reductive groups

1 citations · 2 across the 11 of their papers we have counts for

collaborators

11 papers

math.GR2026

On the representation dimension of finite $p$ -groups

Gurleen Kaur, Amit Kulshrestha, Ayush Udeep

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…

math.GR2024

Chirality and non-real elements in $G_{2} (q)$

Sushil Bhunia, Amit Kulshrestha, Anupam Singh

In this article, we determine the non-real elements--the ones that are not conjugate to their inverses--in the group $G = G_{2} (q)$ when $c ha r (F_{q}) \neq = 2, 3$ . We use this to show that…

math.GR2023

Representation dimension of some finite groups

Gurleen Kaur, Amit Kulshrestha, Anupam Singh

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 repre…

math.RA2022★ 1 cited

Finite Splittings of Differential Matrix Algebras

Amit Kulshrestha, Kanika Singla

It is well known that central simple algebras are split by suitable finite Galois extensions of their centers. A counterpart of this result was studied by Juan and Magid in the set…

math.GR2022

Word Images and Their Impostors in Finite Nilpotent Groups

Dilpreet Kaur, Harish Kishnani, Amit Kulshrestha

It was shown by Lubotzky in 2014 that automorphism invariant subsets of finite simple groups which contain identity are always word images. In this article, we study word maps on f…

math.GR2020★ 1 cited

Asymptotics of the powers in finite reductive groups

Amit Kulshrestha, Rijubrata Kundu, Anupam Singh

Let $G$ be a connected reductive group defined over $F_{q}$ . Fix an integer $M \geq 2$ , and consider the power map $x \mapsto x^{M}$ on $G$ . We denote the image of $G(\mathbb F_q…

math.GR2018

On Shalev's conjecture for type $A_{n}$ and $^{2} A_{n}$

Alexey Galt, Amit Kulshrestha, Anupam Singh +1

In the paper we consider images of finite simple projective special linear and unitary groups under power words. In particular, we show that if $G\simeq \PSL_n^\varepsilon (q)$, th…

math.GR2017

Computing $n^{th}$ roots in $S L_{2}$ and Fibonacci polynomials

Amit Kulshrestha, Anupam Singh

Let $k$ be a field of characteristic $\neq = 2$ . In this paper we study squares, cubes and their products in split and anisotropic groups of type $A_{1}$ . In split case, we show that c…

math.GR2015

Characters of real special 2-groups

Dilpreet Kaur, Amit Kulshrestha

It is well-known that special 2-groups can be described in terms of quadratic maps over fields of characteristic 2. In this article we develop methods to compute conjugacy classes,…

math.GR2012

Strongly real special 2-groups

Dilpreet Kaur, Amit Kulshrestha

Strongly real groups and totally orthogonal groups form two important subclasses of real groups. In this article we give a characterization of strongly real special 2-groups. This…

math.GR2011

Real Elements and Schur Indices of a Group