Fuzzy Group Action on an R-Subgroup in a Near-Ring (Published)
The study investigates the role of group actions on fuzzy R-subgroups within the context of near-rings. Utilizing the notion of fuzzy sets, this research explores the interaction between groups and certain subsets of near-rings, known as R-subgroups. Through the lens of group actions, a deeper understanding of the structural properties and dynamics of fuzzy R-subgroups emerges. Here, we explore group action on a right (respectively left) R subgroup and same type of fuzzy right (respectively left) R-subgroup of a near-ring R, the findings will contribute to the broader field of algebraic structures and provide insights into the interplay between near-rings, groups, and fuzzy set theory
Keywords: Fuzzy Sets, Group Actions, Near-Rings, R-Subgroups, algebraic structures.
On Finding the Number of Homomorphism From Q_8 (Published)
This study investigates the number of homomorphisms from the quaternion group into various finite groups. Quaternion groups, denoted as Q8, possess unique algebraic properties that make them intriguing subjects for group theory inquiries. The research explores the enumeration of homomorphisms from Q8into specific finite groups, providing insights into the structural relationships between these groups. Here, we derive general formulae for counting the number of homomorphisms from quaternion group into each of quaternion group, dihedral group, quasi-dihedral group and modular group by using only elementary group theory
Keywords: algebraic structures., finite groups, group theory, homomorphisms, quaternion group