Units of ℤC_pⁿ

2013/07/19 by Raul Antonio Ferraz, Raul Antônio Ferraz, Ferraz, Raul Antonio +3
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR

paper · pdf · doi:10.48550/arxiv.1307.5229

openalex publication_date 2013/07/19 · arxiv created 2013/07/22 · arxiv updated 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime integer and n,i be positive integers such that \linebreak S=\-1, θ, μ_i=1+θ+... + θ^i-1 | 1 < i < (pⁿ)/(2), gcd(pⁿ,i)=1 \ generates the group of units of ℤ[θ], where θ is a primitive pⁿ--th root of unity. Denote by C_pⁿ the cyclic group of order pⁿ. In this paper we describe explicitly a multiplicatively independent set which generates a complement to ± C_pⁿ in the group of units of the integral group ring of C_pⁿ.

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