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...
| Main Authors: | , , |
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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 |
| Subjects: | |
| Online Access: | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/10346 |
| Summary: | 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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| ISSN: | 2076-1171 2518-0010 |