The application of GAP software in constructing the non-normal subgroup graphs of alternating groups

• Main Authors: Rahin, N. F., Sarmin, Nor Haniza, Ilangovan, S.
• Format: Conference or Workshop Item
• Language: English
• Published: 2022
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/98793/1/NorHanizaSarmin2022_TheApplicationofGAPSoftwareinConstruct.pdf; http://eprints.utm.my/id/eprint/98793/; http://dx.doi.org/10.1088/1742-6596/2287/1/012001
• Institution: Universiti Teknologi Malaysia

A graph in group theory is constructed by using any elements of a group as a set of vertices. Some of the properties of a group are used to form the edges of the graph. A finite group can be represented in a graph by its subgroup structure. A subgroup H of a group G is a subset of G, where H itself is a group under the same operation as in G, whereas a subgroup H is said to be a normal subgroup if its left and right cosets coincide. The non-normal subgroup graph of a group G is defined as a directed graph with a vertex set G and two distinct elements x and y are adjacent if xy H. In this paper, the non-normal subgroups graph of alternating groups for order twelve is determined by using GAP software. The graphs are found to be a union of complete digraphs and directed graphs with the same pattern depending on the order of the non-normal subgroups.