Vipul Kakkar

activity

20122026

p

-Groups of Order

p^{5}

8 citations · 16 across the 23 of their papers we have counts for

collaborators

28 papers

math.GR2026

Determinant for automorphisms of Zappa-Szép product of groups

Ratan Lal, Alka Choudhary, Vipul Kakkar

A description of the endomorphisms of Zappa-Szép products of two groups as a group of $2 \times 2$ matrices of maps is discussed in \cite{detsem}. Using this description, we have st…

math.GR2026

Commutator identities, Lie product identities, and Multiplicative Lie algebras

Vipul Kakkar, Ramji Lal, Ravindra Prasad Shukla +1

The aim of this paper is to give a formal meaning of universal commutator identities and to see as to how the structure of multiplicative Lie algebra on a group is a potential cand…

math.GR2026

Impartial games on two finite Groups

Ratan Lal, Muskan, Vipul Kakkar

In this paper, we study impartial achievement games and impartial avoidance games introduced by Anderson and Harary. Using the criteria of maximal subgroups, we study the game for…

math.GR2025

Determinant for automorphisms of semidirect product of groups

Ratan Lal, Alka Choudhary, Vipul Kakkar

A description of the endomorphisms of semidirect products of two groups as a group of $2 \times 2$ matrices of maps is already known. Using this description, we have studied the con…

math.CO2025

Line Graph Characterization of Cyclic Subgroup Graph

Siddharth Malviy, Vipul Kakkar, Swapnil Srivastava

The cyclic subgroup graph $Γ (G)$ of a group $G$ is the simple undirected graph with cyclic subgroups as a vertex set and two distinct vertices $H_{1}$ and $H_{2}$ are adjacent if and…

math.CO2024

The Minimal (Edge) Connectivity of Some Graphs of Finite Groups

Siddharth Malviy, Vipul Kakkar

In this paper, we classify all the finite groups $G$ such that the commuting graph $Γ_{C} (G)$ , order-sum graph $Γ_{O S} (G)$ and non-inverse graph $Γ_{N I} (G)$ are minimally edge connec…

math.CO2024

Finite groups whose commuting graphs are line graphs

Siddharth Malviy, Vipul Kakkar

The commuting graph $Γ (G)$ of a group $G$ is the simple undirected graph with group elements as a vertex set and two elements $x$ and $y$ are adjacent if and only if $x y = y x$ in $…

math.CO2024

Associating hypergraphs defined on loops

Siddharth Malviy, Vipul Kakkar

In this paper, we define a new hypergraph $H (V, E)$ on a loop $L$ , where $V$ is the set of points of the loop $L$ and $E$ is the set of hyperedges $e=\…

math.GR2024

Semidirect Product of Loops with Groups

Ratan Lal, Ramjash Gurjar, Vipul Kakkar

In this paper, we have studied the loops which are the semidirect products of a loop and a group. Also, the cummutant, nuclei and the center of such loops are studied.

math.GR2023

Gyro-Groups, Gyro-splittings and Co-homology

Ramji Lal, Vipul Kakkar

In this paper, we study gyro-groups associated to groups, group extensions admitting gyro-sections, and corresponding co-homologies. We also describe the obstructions in terms of c…

math.GR2022

Central Automorphisms of Zappa-Szép Products

Ratan Lal, Vipul Kakkar

In this paper, the central automorphism group of the Zappa-Szép product of two groups is obtained.

math.GR2022★ 1 cited

Automorphism groups of groups of order $p^{2} q^{2}$

Ratan Lal, Vipul Kakkar

In this paper, we have computed the automorphism groups of all groups of order $p^{2} q^{2}$ , where $p$ and $q$ are distinct primes.

math.GR2021

Automorphisms of Zappa-Szép Product

Ratan Lal, Vipul Kakkar

In this paper, we have found the automorphism group of the Zappa-Szép product of two groups. Also, we have computed the automorphism group of the Zappa-Szép product of a cyclic gro…

math.GR2021

Automorphisms of semidirect products fixing the non-normal subgroup

Ratan Lal, Vipul Kakkar

In this paper, we describe the automorphism group of semidirect product of two groups that fixes the non-normal subgroup of it. We have computed these automorphisms for the non-abe…

math.GR2021

Gyrogroups associated with groups

Ratan Lal, Vipul Kakkar

In this paper, we study the properties of the associated gyrogroup $^{\circ} G$ of a given group $G$ of nilpotency class $3$ . We have proved that if $3$ does not divide the order of…

math.GR2019★ 5 cited

Schur multipliers of special p-groups of rank 2

Sumana Hatui

A group G is called special p-group of rank k if the commutator subgroup [G,G] and centre Z(G) are equal, which is elementary abelian p-group of rank k and G/[G,G] is also elementa…

math.CO2018

A Construction of Bent Functions on a finite group

Mani Shankar Pandey, Sumit Kumar Upadhyay, Vipul Kakkar

In this paper, we discuss when a class function on a finite group is a bent function. We have found a necessary condition for a class function on a finite abelian group to be bent.…

math.CO2018

On Commuting Graphs of Generalized Dihedral Groups

Vipul Kakkar, Gopal Singh Rawat

For a group $G$ and a subset $X$ of $G$ , the commuting graph of $X$ , denoted by $Γ (G, X)$ is the graph whose vertex set is $X$ and any two vertices $u$ and $v$ in $X$ are adjacent i…

math.GR2018★ 8 cited

The Schur Multipliers of $p$ -Groups of Order $p^{5}$

Sumana Hatui, Vipul Kakkar, Manoj K. Yadav

In this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian $p$ -groups of order $p^{5}$ . As an application we determine the capabil…

math.GR2015

A Study of Groups through Transversals

Vivek Kumar Jain, Vipul Kakkar

In this note, a necessary and sufficient condition for the normalizer of a core-free subgroup $H$ of a finite group $G$ to be normal in $G$ is obtained. Also, a known result of fin…

math.GR2015

Public Key Exchange Using Right Trasversals and Right Loops

Akhilesh Chandra Yadav, Vipul Kakkar

In this article, we describe a key exchange protocol based on right transversals. We also describe it for general extension associated to right loops.

math.GR2014

Solvable and Nilpotent Right Loops

Vivek Kumar Jain, Vipul Kakkar

In this paper the notion of nilpotent right transversal and solvable right transversal has been defined. Further, it is proved that if a core-free subgroup has a generating solvabl…

math.GR2014

On Transiso Graph

Vipul Kakkar, Laxmi Kant Mishra

In this note, we define a new graph $Γ_{d} (G)$ on a finite group $G$ , where $d$ is a divisor of $∣ G ∣$ . The vertices of $Γ_{d} (G)$ are the subgroups of $G$ of order $d$ and two subgroup…

math.GR2013

On the Congruences in Right Loops

Vipul Kakkar, R. P. Shukla

In case the stability relation is a congruence, a necessary and also a sufficient condition for its equality with the center congruence is given.

Determinant for automorphisms of Zappa-Szép product of groups

Commutator identities, Lie product identities, and Multiplicative Lie algebras

Impartial games on two finite Groups

Determinant for automorphisms of semidirect product of groups

Line Graph Characterization of Cyclic Subgroup Graph

The Minimal (Edge) Connectivity of Some Graphs of Finite Groups

Finite groups whose commuting graphs are line graphs

Associating hypergraphs defined on loops

Semidirect Product of Loops with Groups

Gyro-Groups, Gyro-splittings and Co-homology

Central Automorphisms of Zappa-Szép Products

Automorphism groups of groups of order p2q2

Automorphisms of Zappa-Szép Product

Automorphisms of semidirect products fixing the non-normal subgroup

Gyrogroups associated with groups

Schur multipliers of special p-groups of rank 2

A Construction of Bent Functions on a finite group

On Commuting Graphs of Generalized Dihedral Groups

The Schur Multipliers of p-Groups of Order p5

A Study of Groups through Transversals

Public Key Exchange Using Right Trasversals and Right Loops

Solvable and Nilpotent Right Loops

On Transiso Graph

On the Congruences in Right Loops

Automorphism groups of groups of order $p^{2} q^{2}$

The Schur Multipliers of $p$ -Groups of Order $p^{5}$