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The Picture on the Presentation of Direct Product Group of Two Cyclic Groups.
- Source :
-
Journal of Applied Mathematics . 8/31/2023, p1-6. 6p. - Publication Year :
- 2023
-
Abstract
- A picture in a group presentation is a geometric configuration with an arrangement of discs and arcs within a boundary disc. The drawing of this picture does not have to follow a particular rule, only using the generator as discs and the relation as arcs. It will form a picture label pattern if drawn with a particular rule. This paper discusses the label pattern of a picture in the presentation of direct product groups. Direct product presentation is used with two cyclic groups, ℤ p and ℤ q where p , q ∈ ℤ + and p , q ≥ 2. The method for forming a picture label pattern is to arrange the first generator in the initial arrangement, compile a second generator, and add a number of commutators. Furthermore, the pattern is used to calculate the length of the label on the picture. It is obtained that the picture's label is a q − 1 b n a b q − n and the length of the label is p + 2 n − q , where n is the number of commutator discs. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMMUTATORS (Operator theory)
*PICTURES
*COMMUTATION (Electricity)
Subjects
Details
- Language :
- English
- ISSN :
- 1110757X
- Database :
- Academic Search Index
- Journal :
- Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 171352352
- Full Text :
- https://doi.org/10.1155/2023/8018645