Tushar Kanta Naik

activity

20172026

most citedStructure and automorphisms of pure virtual twin groups

9 citations · 35 across the 13 of their papers we have counts for

collaborators

14 papers

math.GR2026

Symmetry and Rigidity of Star-Shaped Coxeter Systems

Arijit Mahato, Tushar Kanta Naik, A Rameswar Patro

We provide a complete description of the automorphism group $\Aut (W)$ of a Coxeter group $W$ admitting a star-shaped finite Coxeter diagram. We prove that each automorphism decomp…

math.GR2024

Linear representations, crystallographic quotients, and twisted conjugacy of virtual Artin groups

Neeraj Kumar Dhanwani, Pravin Kumar, Tushar Kanta Naik +1

Virtual Artin groups were recently introduced by Bellingeri, Paris, and Thiel as broad generalizations of the well-known virtual braid groups. For each Coxeter graph $Γ$ , they defi…

math.GR2023

Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups

Pravin Kumar, Tushar Kanta Naik, Neha Nanda +1

The virtual braid group $V B_{n}$ , the virtual twin group $V T_{n}$ and the virtual triplet group $V L_{n}$ are extensions of the symmetric group $S_{n}$ , which are motivated by the Alexander…

math.GR2022★ 2 cited

Congruence subgroups and crystallographic quotients of small Coxeter groups

Pravin Kumar, Tushar Kanta Naik, Mahender Singh

Small Coxeter groups are precisely the ones for which the Tits representation is integral, which makes the study of their congruence subgroups relevant. The symmetric group $S_{n}$ h…

math.RA2022

Nilpotent Lie algebras with two centralizer dimensions over a finite field

Rijubrata Kundu, Tushar Kanta Naik, Anupam Singh

A result of Barnea and Isaacs states that if $L$ is a finite dimensional nilpotent Lie algebra with exactly two distinct centralizer dimensions, then nilpotency class of $L$ is eit…

math.RA2021★ 1 cited

Nilpotent Lie Algebras of breadth type $(0, 3)$

Rijubrata Kundu, Tushar Kanta Naik, Anupam Singh

For a natural number $m$ , a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0, m)$ if the co-dimension of the centralizer of every non-central element is of dimens…

math.GR2021★ 2 cited

Virtual planar braid groups and permutations

Tushar Kanta Naik, Neha Nanda, Mahender Singh

Twin groups and virtual twin groups are planar analogues of braid groups and virtual braid groups, respectively. These groups play the role of braid groups in the Alexander-Markov…

math.GR2020★ 9 cited

Structure and automorphisms of pure virtual twin groups

Tushar Kanta Naik, Neha Nanda, Mahender Singh

Study of stable isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces is considered as a planar analogue of…

math.GR2020★ 3 cited

Automorphisms of odd Coxeter groups

Tushar Kanta Naik, Mahender Singh

An odd Coxeter group $W$ is one which admits a Coxeter system $(W, S)$ for which all the exponents $m_{ij}$ are either odd or infinity. The paper investigates the family of odd Coxe…

math.GR2019★ 6 cited

Some remarks on twin groups

Tushar Kanta Naik, Neha Nanda, Mahender Singh

The twin group $T_{n}$ is a right angled Coxeter group generated by $n - 1$ involutions and having only far commutativity relations. These groups can be thought of as planar analogues…

math.GR2019★ 8 cited

Conjugacy classes and automorphisms of twin groups

Tushar Kanta Naik, Neha Nanda, Mahender Singh

The twin group $T_{n}$ is a right angled Coxeter group generated by $n - 1$ involutions and the pure twin group $P T_{n}$ is the kernel of the natural surjection from $T_{n}$ onto the symme…

math.GR2018

On the probability distribution associated to commutator word map in finite groups \rom{2}

Tushar Kanta Naik

Let $P (G)$ denotes the set of sizes of fibers of non-trivial commutators of the commutator word map. Here, we prove that $∣ P (G) ∣ = 1$ , for any finite group $G$ of nilpotency class $3…

math.GR2017

Finite $p$ -Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes

Tushar Kanta Naik, Rahul Dattatraya Kitture, Manoj K. Yadav

It is proved that, for a prime $p > 2$ and integer $n \geq 1$ , finite $p$ -groups of nilpotency class $3$ and having only two conjugacy class sizes $1$ and $p^{n}$ exist if and only if $…

math.GR2017★ 4 cited

Finite $p$ -groups of conjugate type ${1, p^{3}}$

Tushar Kanta Naik, Manoj K. Yadav

We classify finite $p$ -groups, upto isoclinism, which have only two conjugacy class sizes $1$ and $p^{3}$ . It turns out that the nilpotency class of such groups is $2$ .

Symmetry and Rigidity of Star-Shaped Coxeter Systems

Linear representations, crystallographic quotients, and twisted conjugacy of virtual Artin groups

Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups

Congruence subgroups and crystallographic quotients of small Coxeter groups

Nilpotent Lie algebras with two centralizer dimensions over a finite field

Nilpotent Lie Algebras of breadth type (0,3)

Virtual planar braid groups and permutations

Structure and automorphisms of pure virtual twin groups

Automorphisms of odd Coxeter groups

Some remarks on twin groups

Conjugacy classes and automorphisms of twin groups

On the probability distribution associated to commutator word map in finite groups \rom{2}

Finite p-Groups of Nilpotency Class 3 with Two Conjugacy Class Sizes

Finite p-groups of conjugate type {1,p3}

Nilpotent Lie Algebras of breadth type $(0, 3)$

Finite $p$ -Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes

Finite $p$ -groups of conjugate type ${1, p^{3}}$