Soft Groups and Characteristic Soft Subgroups
Group theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of the soft group, the kernel of soft homomorphism and s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1450 |
| _version_ | 1797587409787944960 |
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| author | Amlak I. Alajlan Ahmad M. Alghamdi |
| author_facet | Amlak I. Alajlan Ahmad M. Alghamdi |
| author_sort | Amlak I. Alajlan |
| collection | DOAJ |
| description | Group theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of the soft group, the kernel of soft homomorphism and soft automorphisms with their basic properties. Furthermore, the concept of soft point groups is introduced and the properties of these soft groups are studied. We state the concept of characteristic soft subgroups of a given soft group. Also, some theorems related to this concept are investigated. We study the characteristic soft subgroups of a given soft point group. The characteristic soft subgroups play a significant part in the study of the soft group theory and are useful for understanding the structure of a soft group and its soft automorphisms. As an application of characteristic soft subgroups, they allow us to identify and study important soft subgroups that are preserved under soft automorphisms. Also, practical applications for our theory can be conducted in future work such as the relation with other disciplines in sciences. |
| first_indexed | 2024-03-11T00:36:35Z |
| format | Article |
| id | doaj.art-ce6686ef37a541f9b53111af0a4ca51c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:35Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ce6686ef37a541f9b53111af0a4ca51c2023-11-18T21:35:12ZengMDPI AGSymmetry2073-89942023-07-01157145010.3390/sym15071450Soft Groups and Characteristic Soft SubgroupsAmlak I. Alajlan0Ahmad M. Alghamdi1Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi ArabiaDepartment of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi ArabiaGroup theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of the soft group, the kernel of soft homomorphism and soft automorphisms with their basic properties. Furthermore, the concept of soft point groups is introduced and the properties of these soft groups are studied. We state the concept of characteristic soft subgroups of a given soft group. Also, some theorems related to this concept are investigated. We study the characteristic soft subgroups of a given soft point group. The characteristic soft subgroups play a significant part in the study of the soft group theory and are useful for understanding the structure of a soft group and its soft automorphisms. As an application of characteristic soft subgroups, they allow us to identify and study important soft subgroups that are preserved under soft automorphisms. Also, practical applications for our theory can be conducted in future work such as the relation with other disciplines in sciences.https://www.mdpi.com/2073-8994/15/7/1450soft setssoft groupssoft point groupssoft subgroupssoft homomorphismssoft isomorphisms |
| spellingShingle | Amlak I. Alajlan Ahmad M. Alghamdi Soft Groups and Characteristic Soft Subgroups Symmetry soft sets soft groups soft point groups soft subgroups soft homomorphisms soft isomorphisms |
| title | Soft Groups and Characteristic Soft Subgroups |
| title_full | Soft Groups and Characteristic Soft Subgroups |
| title_fullStr | Soft Groups and Characteristic Soft Subgroups |
| title_full_unstemmed | Soft Groups and Characteristic Soft Subgroups |
| title_short | Soft Groups and Characteristic Soft Subgroups |
| title_sort | soft groups and characteristic soft subgroups |
| topic | soft sets soft groups soft point groups soft subgroups soft homomorphisms soft isomorphisms |
| url | https://www.mdpi.com/2073-8994/15/7/1450 |
| work_keys_str_mv | AT amlakialajlan softgroupsandcharacteristicsoftsubgroups AT ahmadmalghamdi softgroupsandcharacteristicsoftsubgroups |