The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10)
In this paper, we propose the cyclic decomposition of the factor group cf(Q2q×C10)‚Z)/R ̅(Q2q×C10 ), and the group cf(Q2q×C10‚Z) is Z-valued class functions of the direct product group ((Q14×C10)) under the operation of addition, and R((Q14×C10)) is the subgroup of the generalized characters of the...
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| Format: | Article |
| Language: | English |
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Faculty of Computer Science and Mathematics, University of Kufa
2022-03-01
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| Series: | Journal of Kufa for Mathematics and Computer |
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| Online Access: | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/10346 |
| _version_ | 1797267004693938176 |
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| author | Naseer Albakaa Habeeb Al-Bdairi Neeran Abd Alameer |
| author_facet | Naseer Albakaa Habeeb Al-Bdairi Neeran Abd Alameer |
| author_sort | Naseer Albakaa |
| collection | DOAJ |
| description |
In this paper, we propose the cyclic decomposition of the factor group cf(Q2q×C10)‚Z)/R ̅(Q2q×C10 ), and the group cf(Q2q×C10‚Z) is Z-valued class functions of the direct product group ((Q14×C10)) under the operation of addition, and R((Q14×C10)) is the subgroup of the generalized characters of the group cf(Q2q×C10)‚Z).Then cf(Q2q×C10‚Z)/(R() ̅Q2q×C10)) is an abelian factor group denoted by K(Q2q×C10)) where (Q14 is the quaternion group of order28 and C10 is the cyclic group of order 10. Also, we find the rational valued characters table of the group (Q2q×C10 ) when p, and q prime numbers and s∈Z^+ is given as follows : ≡^* (Q2q×C10))=〖 ≡〗^* ((Q14 )⨂≡^* (C10 ) (1) and find the cyclic decomposition of group (Q2q×C10 ) in this paper and prove that K(Q2q×C10 )=⨁_(i=1)^4 [KQ2q ] ⨁_(i=1)^5 K (C10 ) (2)
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| first_indexed | 2024-04-25T01:09:42Z |
| format | Article |
| id | doaj.art-be2a5ea858564225b5efaab974c6e0bf |
| institution | Directory Open Access Journal |
| issn | 2076-1171 2518-0010 |
| language | English |
| last_indexed | 2024-04-25T01:09:42Z |
| publishDate | 2022-03-01 |
| publisher | Faculty of Computer Science and Mathematics, University of Kufa |
| record_format | Article |
| series | Journal of Kufa for Mathematics and Computer |
| spelling | doaj.art-be2a5ea858564225b5efaab974c6e0bf2024-03-10T10:20:12ZengFaculty of Computer Science and Mathematics, University of KufaJournal of Kufa for Mathematics and Computer2076-11712518-00102022-03-019110.31642/JoKMC/2018/090104The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10)Naseer Albakaa0Habeeb Al-Bdairi1Neeran Abd Alameer 2University of KufaUniversity of KufaUniversity of Kufa In this paper, we propose the cyclic decomposition of the factor group cf(Q2q×C10)‚Z)/R ̅(Q2q×C10 ), and the group cf(Q2q×C10‚Z) is Z-valued class functions of the direct product group ((Q14×C10)) under the operation of addition, and R((Q14×C10)) is the subgroup of the generalized characters of the group cf(Q2q×C10)‚Z).Then cf(Q2q×C10‚Z)/(R() ̅Q2q×C10)) is an abelian factor group denoted by K(Q2q×C10)) where (Q14 is the quaternion group of order28 and C10 is the cyclic group of order 10. Also, we find the rational valued characters table of the group (Q2q×C10 ) when p, and q prime numbers and s∈Z^+ is given as follows : ≡^* (Q2q×C10))=〖 ≡〗^* ((Q14 )⨂≡^* (C10 ) (1) and find the cyclic decomposition of group (Q2q×C10 ) in this paper and prove that K(Q2q×C10 )=⨁_(i=1)^4 [KQ2q ] ⨁_(i=1)^5 K (C10 ) (2) https://journal.uokufa.edu.iq/index.php/jkmc/article/view/10346matrix representationcharacter tablesQuaternion groupsthe cyclic decomposition of group |
| spellingShingle | Naseer Albakaa Habeeb Al-Bdairi Neeran Abd Alameer The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10) Journal of Kufa for Mathematics and Computer matrix representation character tables Quaternion groups the cyclic decomposition of group |
| title | The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10) |
| title_full | The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10) |
| title_fullStr | The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10) |
| title_full_unstemmed | The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10) |
| title_short | The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10) |
| title_sort | cyclic decomposition of cf q2q c10 r ̅ q29 c10 |
| topic | matrix representation character tables Quaternion groups the cyclic decomposition of group |
| url | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/10346 |
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