The Cyclic Decomposition Of cf(Q_14×C_2p)/ R ̅(Q_14×C_2p)

  • Naseer Albakaa University of kufa
  • Habeeb Kareem Al-Bdairi
  • Neeran Tahir Abd Alameer
Keywords: matrix representation, character tables, Quaternion groups, the cyclic decomposition of group.

Abstract

. In this paper, we propose the cyclic decomposition of the factor group , and the group  is Z-valued class functions of the direct product group  under the operation of addition, and  is the subgroup of the generalized characters of the group .Then   is an abelian factor group denoted by  where  is the quaternion group of order  and  is the cyclic  group of order . Also, we find the  rational  valued  characters  table  of  the  group  when  and   prime  numbers and  is  given  as  follows :

 

 

(1)

and find the cyclic decomposition of  group  in this paper and prove that

 

 

(2)

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References

1 C.Curits and I.Reiner ," Methods of Representation Theory with Application to Finite Groups and Order " , John wily& sons, New York, 1981.
2 H.H. Abass," On The Factor Group of Class Functions Over The Group of Generalized Characters of Dn", M.Sc thesis, Technology University,1994.
3 J. P. Serre, " Linear Representation of Finite Groups " ,Springer- Verlage, 1977.
4 M.S. Kirdar , " The Factor Group of The Z-Valued Class Function Modulo The Group of The Generalized Characters" , Ph.D . thesis, University of Birmingham ,1982 .
5 M. S. Mahdi ,( 2008) "The Cyclic Decomposition of The Factor Group cf(Dnh,Z)/ R ̅ (Dnh) When n is an Odd Number", M.Sc. Thesis, University of Kufa.
6 N. R. Mahamood " The Cyclic Decomposition of the Factor Group cf(Q_2m,Z)/R ̅(Q_2m)", M.Sc. thesis, University of Technology, 1995.
7 N. A. Rahi ,( 2013) "On Cyclic Decomposition of The Group cf(Q2m×C5,Z)/ R ̅(Q2m×C5) When m is An odd Number", M.Sc. Thesis, University of Kufa.
Published
2022-01-30
How to Cite
Albakaa, N., Habeeb Kareem Al-Bdairi, & Tahir Abd Alameer, N. (2022). The Cyclic Decomposition Of cf(Q_14×C_2p)/ R ̅(Q_14×C_2p) . Al-Qadisiyah Journal of Pure Science, 27(1), Math 41-50. https://doi.org/10.29350/qjps.2022.27.1.1475
Section
Mathematics

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