Sunil Kumar Prajapati

activity

20192025

most citedSimultaneous Conjugacy Classes of Finite

p

-groups of rank

\leq 5

2 citations · 3 across the 13 of their papers we have counts for

collaborators

13 papers

math.RT2025

A Combinatorial Technique for the Wedderburn Decomposition of Rational Group Algebras of Nested GVZ $p$ -groups

Ram Karan Choudhary, Sunil Kumar Prajapati

In this article, we present a combinatorial formula for the Wedderburn decomposition of rational group algebras of nested GVZ $p$ -groups, where $p$ is an odd prime. Using this form…

math.RT2025

Rational Group Algebras of Camina $p$ -groups

Ram Karan Choudhary, Sunil Kumar Prajapati

In this article, we present a combinatorial formula for the Wedderburn decomposition of rational group algebras of Camina $p$ -groups, where $p$ is a prime. We also provide a comple…

math.RT2024

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$ -groups

Ram Karan Choudhary, Sunil Kumar Prajapati

In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic $p$ -group $G$ , w…

math.GR2024

Exceptional groups of order $p^{6}$ for primes $p \geq 5$

E. A. O'Brien, Sunil Kumar Prajapati, Ayush Udeep

The minimal faithful permutation degree $μ (G)$ of a finite group $G$ is the least integer $n$ such that $G$ is isomorphic to a subgroup of the symmetric group $S_{n}$ . If $G$ has a n…

math.RT2024

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras of Split Metacyclic $p$ -groups

Ram Karan Choudhary, Sunil Kumar Prajapati

In this article, we present a concise combinatorial formula for efficiently determining the Wedderburn decomposition of rational group algebra associated with a split metacyclic $p…

math.RT2023

Rational Representations and Rational Group Algebra of VZ p-groups

Ram Karan Choudhary, Sunil Kumar Prajapati

In this article, we study rational matrix representations of VZ $p$ -groups ( $p$ is any prime). Utilizing our findings on VZ $p$ -groups, we explicitly obtain all inequivalent irredu…

math.GR2023

Comment on: The groups of order $p^{6}$ ( $p$ an odd prime) By Rodney James, Math. Comput. 34 (1980), 613-637

E. A. O'Brien, Sunil Kumar Prajapati, Ayush Udeep

Over the years various errors have been identified in the 1980 paper of James on the groups of order $p^{6}$ , where $p$ is an odd prime. Here we summarise them.

math.GR2023★ 1 cited

Minimal degrees for faithful permutation representations of groups of order $p^{6}$ where $p$ is an odd prime

E. A. O'Brien, Sunil Kumar Prajapati, Ayush Udeep

We determine the minimal degree of a faithful permutation representation for each group of order $p^{6}$ where $p$ is an odd prime. We also record how to obtain such a representation…

math.GR2023

On the relation of character codegrees and the minimal faithful quasi-permutation representation degree of $p$ -groups

Sunil Kumar Prajapati, Ayush Udeep

For a finite group $G$ , we denote by $c (G)$ , the minimal degree of faithful representation of $G$ by quasi-permutation matrices over the complex field $C$ . For an irreduci…

math.GR2023

Minimal Faithful Quasi-Permutation Representation Degree of p-Groups with Cyclic Center

Sunil Kumar Prajapati, Ayush Udeep

For a finite group G, we denote by $μ (G)$ , and c(G), the minimal degree of faithful permutation representation of G, and the minimal degree of faithful representation of G by quasi…

math.GR2021

On faithful quasi-permutation representations of $V Z$ -groups and Camina $p$ -groups

Sunil Kumar Prajapati, Ayush Udeep

For a finite group $G$ , we denote by $μ (G)$ and $c (G),$ the minimal degree of faithful permutation representation of $G$ and the minimal degree of faithful representation of $G$ by…

math.GR2021★ 2 cited

Simultaneous Conjugacy Classes of Finite $p$ -groups of rank $\leq 5$

Dilpreet Kaur, Sunil Kumar Prajapati, Amritanshu Prasad

For a finite group $G$ , we consider the problem of counting simultaneous conjugacy classes of $n$ -tuples and simultaneous conjugacy classes of commuting $n$ -tuples in $G$ . Let $α_{…

math.GR2019

Simultaneous Conjugacy Classes as Combinatorial Invariants of Finite Groups

Dilpreet Kaur, Sunil Kumar Prajapati, Amritanshu Prasad

Let $G$ be a finite group. We consider the problem of counting simultaneous conjugacy classes of $n$ -tuples and simultaneous conjugacy classes of commuting $n$ -tuples in $G$ . Let $…

A Combinatorial Technique for the Wedderburn Decomposition of Rational Group Algebras of Nested GVZ p-groups

Rational Group Algebras of Camina p-groups

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic p-groups

Exceptional groups of order p6 for primes p≥5

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras of Split Metacyclic p-groups

Rational Representations and Rational Group Algebra of VZ p-groups

Comment on: The groups of order p6 (p an odd prime) By Rodney James, Math. Comput. 34 (1980), 613-637

Minimal degrees for faithful permutation representations of groups of order p6 where p is an odd prime

On the relation of character codegrees and the minimal faithful quasi-permutation representation degree of p-groups

Minimal Faithful Quasi-Permutation Representation Degree of p-Groups with Cyclic Center

On faithful quasi-permutation representations of VZ-groups and Camina p-groups

Simultaneous Conjugacy Classes of Finite p-groups of rank ≤5

Simultaneous Conjugacy Classes as Combinatorial Invariants of Finite Groups

A Combinatorial Technique for the Wedderburn Decomposition of Rational Group Algebras of Nested GVZ $p$ -groups

Rational Group Algebras of Camina $p$ -groups

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic $p$ -groups

Exceptional groups of order $p^{6}$ for primes $p \geq 5$

A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras of Split Metacyclic $p$ -groups

Comment on: The groups of order $p^{6}$ ( $p$ an odd prime) By Rodney James, Math. Comput. 34 (1980), 613-637

Minimal degrees for faithful permutation representations of groups of order $p^{6}$ where $p$ is an odd prime

On the relation of character codegrees and the minimal faithful quasi-permutation representation degree of $p$ -groups

On faithful quasi-permutation representations of $V Z$ -groups and Camina $p$ -groups

Simultaneous Conjugacy Classes of Finite $p$ -groups of rank $\leq 5$