The application of GAP software in constructing the non-normal subgroup graphs of alternating groups
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...
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| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| 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 |
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| Institution: | Universiti Teknologi Malaysia |
| Language: | English |
| Summary: | 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. |
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