COMPUTATIONAL ANALYSIS OF THE NON-NORMAL CYCLIC SUBGROUP GRAPH OF THE QUASIDIHEDRAL GROUP OF ORDER 32 USING GAP AND MAPLE SOFTWARE
DOI:
https://doi.org/10.35631/IJIREV.825035Keywords:
Graph Theory, Group Theory, Quasidihedral Group, Subgroup GraphAbstract
Let G be a group and H be a non-normal cyclic subgroup of G. The non-normal cyclic subgroup graph, denoted as {\Gamma }_{H}^{NN}(G), is defined as a directed graph with vertex set elements of G such that for two distinct elements x and y in G, x is the initial vertex and y is the terminal vertex of an edge if their product is in H. In this presentation, the non-normal cyclic subgroup graphs for the quasidihedral group of order 32 are constructed. Firstly, the non-normal subgroups of quasidihedral groups of order 32 are determined using the Groups, Algorithms and Programming (GAP) software where the identification of the non-normal cyclic subgroups is carried out. Subsequently, the definition of the non-normal cyclic subgroup graph is applied to compute the directions of the vertices of the graph and Maple 2016 is used for graph visualization. The results show that there are several different graph patterns arise from these subgroups.
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