8 citations · 16 across the 23 of their papers we have counts for
22 papers · 1 filter
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 matrices of maps is discussed in \cite{detsem}. Using this description, we have st…
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…
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…
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 matrices of maps is already known. Using this description, we have studied the con…
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.
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…
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.
Automorphism groups of groups of order
Ratan Lal, Vipul Kakkar
In this paper, we have computed the automorphism groups of all groups of order , where and are distinct primes.
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…
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…
Gyrogroups associated with groups
Ratan Lal, Vipul Kakkar
In this paper, we study the properties of the associated gyrogroup of a given group of nilpotency class . We have proved that if does not divide the order of…
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…
The Schur Multipliers of -Groups of Order
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 -groups of order . As an application we determine the capabil…
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 of a finite group to be normal in is obtained. Also, a known result of fin…
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.
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…
On Transiso Graph
Vipul Kakkar, Laxmi Kant Mishra
In this note, we define a new graph on a finite group , where is a divisor of . The vertices of are the subgroups of of order and two subgroup…
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.
An Example of a Right Loop Admitting Only Discrete Topolization
Vipul Kakkar
Being motivated by \cite{sk} and \cite{nms}, an example of a right loop admitting only discrete topolization is given.
Isotopic classes of Transversals
Vipul Kakkar, R. P. Shukla
Let be a finite group and be a subgroup of . In this paper, we prove that if is a finite nilpotent group and a subgroup of , then is normal in if and…
On the Number of Isomorphism Classes of Transversals
Vipul Kakkar, R. P. Shukla
In this paper we prove that there does not exist a subgroup of a finite group such that the number of isomorphism classes of normalized right transversals of in is…
Some Characterizations of a Normal Subgroup of a Group
Vipul Kakkar, R. P. Shukla
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we…