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

Authors

  • Rajaa Hassan Abass
  • . .

DOI:

https://doi.org/10.14419/ijet.v7i4.36.24223

Published:

2018-12-09

Keywords:

Quaternion group, the cyclic group, Artin's characters, Artin's characters table, the cyclic decomposition

Abstract

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] 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).

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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
Received 2018-12-18
Accepted 2018-12-18
Published 2018-12-09