Graph of Co-Maximal Subgroups in The Integer Modulo N Group (Published)
This research delves into the co-maximal subgroup graph of the integer modulo group, . Investigating the structural properties of this graph provides insights into the relationships among subgroups of . We explore the connectivity, patterns, and specific cases, offering a comprehensive analysis of this algebraic structure. Through a combination of group theory and graph theory, we aim to contribute to the broader understanding of subgroup interactions in cyclic groups.
Keywords: Co-maximal subgroups, cyclic groups, graph theory, group theory, integer modulo n, subgroup graph
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