2023/05/03 by Louis Mallet-Burgues, Mallet-Burgues, Louis
Computer Science · Engineering · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.01987
openalex publication_date 2023/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The article presents several methods for the arithmetic of finite abelian groups. We introduce a tool - already used by Delsarte in [1] as I found out later - analogous to Dirichlet's convolution to obtain combinatorial results on these groups. Using this convolution and some group actions, we deduce an interesting fact : the number of generating subsets of a finite abelian group is always a multiple of the order of the group. Eventually, we prove a theorem about the generation of the group of permutations of an abelian group G using only transpositions and translations from the group G.