2020/03/30 by Kevin Zhao, Zhao, Kevin
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2003.13290
openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group. We will say that M and S form a complete splitting (splitting) of G if every element (nonzero element) g of G has a unique representation of the form g=ms with m∈ M and s∈ S, and 0 has a such representation (while 0 has no such representation). In this paper, we determine the structures of complete splittings of finite abelian groups. In particular, for complete splittings of cyclic groups our description is more specific. Furthermore, we show some results for existence and nonexistence of complete splittings of cyclic groups and find a relationship between complete splittings and splittings for finite groups.