A Way to Construct Commutative Hyperstructures
This article aims to create commutative hyperstructures, starting with a non-commutative group. Therefore, we consider the starting group to be the dihedral group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><ms...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Computer Sciences & Mathematics Forum |
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| Online Access: | https://www.mdpi.com/2813-0324/7/1/22 |
| _version_ | 1827575103198593024 |
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| author | Andromeda Sonea |
| author_facet | Andromeda Sonea |
| author_sort | Andromeda Sonea |
| collection | DOAJ |
| description | This article aims to create commutative hyperstructures, starting with a non-commutative group. Therefore, we consider the starting group to be the dihedral group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>n</mi></msub></semantics></math></inline-formula>, where <i>n</i> is a natural number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, and we determine the HX groups associated with the dihedral group. For a fixed number <i>n</i>, we note <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">G</mi><mi>n</mi></msub><mo>=</mo><mfenced separators="" open="{" close="}"><msubsup><mi mathvariant="script">G</mi><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow><msub><mi>p</mi><mn>1</mn></msub></msubsup><mspace width="4.pt"></mspace><mi>H</mi><mi>X</mi><mo>−</mo><mrow><mi>groups</mi><mo>,</mo></mrow><mspace width="4.pt"></mspace><mi>for</mi><mspace width="4.pt"></mspace><mi>any</mi><mspace width="4.pt"></mspace><msub><mi>p</mi><mn>1</mn></msub><mo>,</mo><mspace width="4.pt"></mspace><msub><mi>p</mi><mn>2</mn></msub><mo>∈</mo><msup><mi mathvariant="double-struck">N</mi><mo>*</mo></msup><mspace width="4.pt"></mspace><mi>such</mi><mspace width="4.pt"></mspace><mi>that</mi><mspace width="4.pt"></mspace><mi>n</mi><mo>=</mo><msub><mi>p</mi><mn>1</mn></msub><msub><mi>p</mi><mn>2</mn></msub></mfenced></mrow></semantics></math></inline-formula> as the set of all HX groups. This paper analyses this new structure’s properties for particular cases when the dihedral group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mn>4</mn></msub></semantics></math></inline-formula> is the support group. |
| first_indexed | 2024-03-08T20:52:29Z |
| format | Article |
| id | doaj.art-2779b04cac0c439585e899d253685387 |
| institution | Directory Open Access Journal |
| issn | 2813-0324 |
| language | English |
| last_indexed | 2024-03-08T20:52:29Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computer Sciences & Mathematics Forum |
| spelling | doaj.art-2779b04cac0c439585e899d2536853872023-12-22T14:02:06ZengMDPI AGComputer Sciences & Mathematics Forum2813-03242023-04-01712210.3390/IOCMA2023-14385A Way to Construct Commutative HyperstructuresAndromeda Sonea0Department of Sciences, Faculty of Horticulture, Iasi University of Life Sciences, 700490 Iasi, RomaniaThis article aims to create commutative hyperstructures, starting with a non-commutative group. Therefore, we consider the starting group to be the dihedral group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>n</mi></msub></semantics></math></inline-formula>, where <i>n</i> is a natural number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, and we determine the HX groups associated with the dihedral group. For a fixed number <i>n</i>, we note <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">G</mi><mi>n</mi></msub><mo>=</mo><mfenced separators="" open="{" close="}"><msubsup><mi mathvariant="script">G</mi><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow><msub><mi>p</mi><mn>1</mn></msub></msubsup><mspace width="4.pt"></mspace><mi>H</mi><mi>X</mi><mo>−</mo><mrow><mi>groups</mi><mo>,</mo></mrow><mspace width="4.pt"></mspace><mi>for</mi><mspace width="4.pt"></mspace><mi>any</mi><mspace width="4.pt"></mspace><msub><mi>p</mi><mn>1</mn></msub><mo>,</mo><mspace width="4.pt"></mspace><msub><mi>p</mi><mn>2</mn></msub><mo>∈</mo><msup><mi mathvariant="double-struck">N</mi><mo>*</mo></msup><mspace width="4.pt"></mspace><mi>such</mi><mspace width="4.pt"></mspace><mi>that</mi><mspace width="4.pt"></mspace><mi>n</mi><mo>=</mo><msub><mi>p</mi><mn>1</mn></msub><msub><mi>p</mi><mn>2</mn></msub></mfenced></mrow></semantics></math></inline-formula> as the set of all HX groups. This paper analyses this new structure’s properties for particular cases when the dihedral group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mn>4</mn></msub></semantics></math></inline-formula> is the support group.https://www.mdpi.com/2813-0324/7/1/22HX-groupsdihedral groupcommutativityhyperstructures |
| spellingShingle | Andromeda Sonea A Way to Construct Commutative Hyperstructures Computer Sciences & Mathematics Forum HX-groups dihedral group commutativity hyperstructures |
| title | A Way to Construct Commutative Hyperstructures |
| title_full | A Way to Construct Commutative Hyperstructures |
| title_fullStr | A Way to Construct Commutative Hyperstructures |
| title_full_unstemmed | A Way to Construct Commutative Hyperstructures |
| title_short | A Way to Construct Commutative Hyperstructures |
| title_sort | way to construct commutative hyperstructures |
| topic | HX-groups dihedral group commutativity hyperstructures |
| url | https://www.mdpi.com/2813-0324/7/1/22 |
| work_keys_str_mv | AT andromedasonea awaytoconstructcommutativehyperstructures AT andromedasonea waytoconstructcommutativehyperstructures |