On Artin Cokernel of The Quaternion Group Q2m When m=2^h ,h any positive integers Number

Authors

  • Sahar Jaafar Mahmood Department of Mathematics College of Computer Science and Information Technology University of Al_Qadisiyah
  • Nesir Rasool Mahmood Department of Mathematics College of Education for Girls University of Kufa

Keywords:

Artin cokernel, Quaternion group, cyclic decomposition, Artin characters

Abstract

In this article we find the cyclic decomposition of the finite abelian factor group AC(G)= R (G)/T(G) where G = Q2m and 2h m  ,
h any positive integers and Q2m is the Quaternion group of order 4m.
(the group of all Z-valued generalized characters of G over the group of induced unit characters from all cyclic subgroups of G) .
We find that the cyclic decomposition AC(Q2m) depends on the elementary divisor of m
If 2h m  , h any positive integers , then :
AC(Q2m)=1
1
h
i

 
C2
Moreover, we have also found the general form of Artin characters table Ar(Q2m) when m is an even number .

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Published

2022-03-17

How to Cite

Mahmood, S., & Mahmood, N. (2022). On Artin Cokernel of The Quaternion Group Q2m When m=2^h ,h any positive integers Number. Journal of Iraqi AL-Khwarizmi, 2(special), 205–219. Retrieved from https://iraqma.net/journal/index.php/JIKhs/article/view/49

Issue

Vol. 2 No. special (2018): special

Section

Articles