Rahin, N. F. and Sarmin, Nor Haniza and Ilangovan, S. (2022) The application of GAP software in constructing the nonnormal subgroup graphs of alternating groups. In: 12th International Conference on Applied Physics and Mathematics, ICAPM 2022, 18 February 2022  20 February 2022, Singapore, Virtual, Online.

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Official URL: http://dx.doi.org/10.1088/17426596/2287/1/012001
Abstract
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 nonnormal 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 nonnormal 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 nonnormal subgroups.
Item Type:  Conference or Workshop Item (Paper) 

Uncontrolled Keywords:  finite groups, property, subgroup structure, vertex set 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  98793 
Deposited By:  Yanti Mohd Shah 
Deposited On:  02 Feb 2023 08:53 
Last Modified:  02 Feb 2023 08:53 
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