On Artin Cokernel of The Group Dn×C7 When n is an Odd Number

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Muthanna Journal of Pure Sciences – MJPS

 

VOL.(3), NO.(2), 2016

Amer Khraja Abed Al-shypany
Al-muthanna Education, Ministry of Education

 

Abstract

The group of all Z-valued generalized characters of G over the group of induced unit characters from all
cyclic subgroups of G, AC(G)= ̅ (G)/T(G) forms a finite abelian group, called Artin Cokernel of G .The problem of finding the cyclic decomposition of Artin cokernel AC(Dn×C7) has been considered in this paper when n is an odd number , we find that if n = 1 1 .1 2 .. , where p1,p2,…, pm are distinct primes and not equal to 2 , then :
2((1 + 1).(2 + 1)…( + 1)) -1
AC(Dn×C7) =  ⨁  = 1    C2
= 2 ⨁ = 1 AC(Dn) ⨁ C2
And we give the general form of Artin’s characters table Ar (Dn×C7)when n is an odd number.

Keywords: Group, cyclic group, Artin cokernel.


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