On Artin Cokernel of the Quaternion Group Q_{2m} when m=2^h \cdot p_{1}^{r_1} \cdot p_{2}^{r_2} \cdots p_{n}^{r_n} such that p_i are Primes, g.c.d.(p_i, p_j)=1 and p_i \neq 2 for all i = 1, 2, ..., n, h and r_i any Positive Integer Numbers

  • Sahar Jaafar Mahmood Department of Mathematics, College of Computer Science and Information Technology, University of Al_Qadisiyah, Iraq
  • Nesir Rasool Mahmood Department of Mathematics, College of Education for Girls, University of Kufa, Iraq
  • Dhirgam Allawy Hussein Directorate of Education in Al_Qadisiyah, Iraq
DOI: https://doi.org/10.34198/ejms.4120.169188
Keywords: Artin cokernel, quaternion group, cyclic decomposition, Artin characters

Abstract

In this article, we find the cyclic decomposition of the finite abelian factor group 1.PNG where 2.PNG and m is an even number and 3.PNG 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 4.PNG depends on the elementary divisor of m. We have found that if 5.PNG are distinct primes, then:

6.PNG

Moreover, we have also found the general form of Artin characters table 7.PNG when m is an even number.

Published
2020-04-30
How to Cite
Mahmood, S. J., Mahmood, N. R., & Hussein, D. A. (2020). On Artin Cokernel of the Quaternion Group Q_{2m} when m=2^h \cdot p_{1}^{r_1} \cdot p_{2}^{r_2} \cdots p_{n}^{r_n} such that p_i are Primes, g.c.d.(p_i, p_j)=1 and p_i \neq 2 for all i = 1, 2, ., n, h and r_i any Positive Integer Numbers. Earthline Journal of Mathematical Sciences, 4(1), 169-188. https://doi.org/10.34198/ejms.4120.169188
Issue
Vol 4 No 1 (2020)
Section
Articles


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