11 citations · 17 across the 12 of their papers we have counts for
12 papers
On the number of orthomorphisms of the alternating group on four symbols
Vivek Kumar Jain, Rohitesh Pradhan
In this study, the set of orthomorphisms of a finite group G of order 3M with a normal subgroup of order M has been partitioned into classes. Additionally, a number of relationship…
A Characterization of Group Through Isomorphism Classes of Transversals
Vivek Kumar Jain, Raja Rawat
Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index…
The Structure of Orthomorphism Graph of
Rohitesh Pradhan, Vivek Kumar Jain
In this paper, we gave a theoretical proof of the fact that Orthomorphism graph of group has maximal clique 2, by determining the structure of th…
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…
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…
A Note On Transversals
Vivek Kumar Jain
Let be a finite group and a core-free subgroup of . We will show that if there exists a solvable, generating transversal of in , then is a solvable group. Fur…