The Cyclic decomposition and the Artin characters table of the group (Q2m Cp) when m=2h , h ∈ Z+ and p is prime number
Journal of Al-Qadisiyah for Computer Science and Mathematics,
2016, Volume 8, Issue 1, Pages 25-42
AbstractThe main purpose of this paper, is determination of the cyclic decomposition of the abelian factor group AC(G) = (G)/T(G) where G = Q2m×Cp when m=2h , h ∈ Z+ and p is prime number (the group of all Z-valued characters of G over the group of induced unit characters from all cyclic subgroups of G).
We have found that the cyclic decomposition AC(Q2m×Cp) depends on the elementary divisor of m as follows.
if m = 2 , h any positive integer and p is prime number, then:
AC( Q2m×Cp) =
We have also found the general form of Artin's characters table of Ar(Q2m×Cp) when m=2h , h ∈ Z+ and p is prime
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