Study of Artin Cokernel of the Group (𝑫𝒏 × 𝑪𝟏𝟏), Where n is an Even Number

Bassim Kareem Mihsin · 2023

In this work,we find the cyclic decomposition of Artin Cokernel 𝐴𝐶(𝐷𝑛 × 𝐶11) where 𝑛 is an even number and we find the Artin characters table 𝐴𝑟(𝐷𝑛 × 𝐶11), where 𝑛 is an even number such that ; 𝑛 = 𝑞1 𝜏1 ∙ 𝑞2 𝜏2 … 𝑞𝑚 𝜏𝑚 ∙ 2 𝛾 , 𝑞𝑖 ≠ 2 and 𝑞𝑖 are distinct primes for all 𝑖 = 1, 2, 3, … , 𝑚 ,then: 𝐴𝐶(𝐷𝑛 × 𝐶11) = 2(𝜏1 +1)(𝜏2 + 1) ⋯ (𝜏𝑚 +1)(𝛾 + 1 +)− 1 ⊕ 𝑖 = 1 𝐶2 and if 𝑛 = 2 𝛾 , 𝛾 is any positive integer then 𝐴𝐶(𝐷𝑛 × 𝐶11) = 2𝛾 ⊕ 𝑖 = 1 𝐶2

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