The Cyclic Decomposition of the Group (Q2m C4) When m= ,h, r∈ Z+ and p is Prime Number

  • Authors

    • Rajaa Hassan Abass
    • . .
    2018-12-09
    https://doi.org/10.14419/ijet.v7i4.36.24223
  • Quaternion group, the cyclic group, Artin's characters, Artin's characters table, the cyclic decomposition
  • The main purpose of this paper is to find The Cyclic decomposition of the group (Q2m C4) when m= h, r  Z+and p is prime number, which is denoted by AC (Q2m ×C4) where Q2m is the Quaternion group and C4 is the cyclic group of order 4 . We have also found the general form of Artin's characters table of Ar(Q2m×C4) when m=  ,h,r  Z+and p is prime number.

     


  • References

    1. [1] Mohammed AH, On Artin Cokernel of finite Groups, M.Sc. thesis, University of Kufa, (2007).

      [2] Abid AS, Artin's Characters Table of Dihedral Group for Odd Number, M.Sc. thesis, University Kufa, (2006).

      [3] Curits C & Reiner I, Methods of Representation Theory with Application to Finite Groups and Order, John wily & sons, New York, (1981).

      [4] Curits CW & Renier I, Representation Theory of Fi­nite Groups and Associative Algebra, AMS Chelsea publishing, (1962).

      [5] Yassien HR, On Artin Cokernel of Finite Group, M.Sc. thesis, Babylon University, (2000).

      [6] Isaacs IM, On Character Theory of Finite Groups, Academic Press, New York, (1976).

      [7] Sekiguchi K, “Extensions and the irreducibilities of the induced characters of cyclic $ p $-groupsâ€, Hiroshima Mathematical Journal, Vol.32, No.2, (2002), pp.165-178.

      [8] Hall MJ, The Theory of Group, Macmillan, New York, (1959).

      [9] Abass RH, “On the Rational Valued Characters Table of the Group (Q2m×C4) When m is an Even Numberâ€, Applied Mathematical Sciences, (2017), pp.1915–1923.

      [10] Mahmood SJ, On Artin Cokernel of Quaternion Group Q2m when m is an Even Number, M.Sc. thesis, University of Kufa, 2009.

      [11] Lam TY, “Artin Exponent of Finite Groupsâ€, Columbia University, New York, (1967).

  • Downloads

  • How to Cite

    Hassan Abass, R., & ., . (2018). The Cyclic Decomposition of the Group (Q2m C4) When m= ,h, r∈ Z+ and p is Prime Number. International Journal of Engineering & Technology, 7(4.36), 681-688. https://doi.org/10.14419/ijet.v7i4.36.24223