Some New Results on Purely Singular Splittings  

作　　者：Pingzhi Yuan 

机构地区：[1]School of Mathematical Science,South China Normal University,Guangzhou 510631,China

出　　处：《Communications in Mathematical Research》2022年第2期136-156,共21页数学研究通讯（英文版）

摘　　要：Let G be a finite abelian group,M a set of integers and S a subset of G.We say that M and S form a splitting of G if every nonzero element g of G has a unique representation of the form g=m s with m∈M and s∈S,while 0 has no such representation.The splitting is called purely singular if for each prime divisor p of|G|,there is at least one element of M is divisible by p.In this paper,we continue the study of purely singular splittings of cyclic groups.We prove that if k≥2 is a positive integer such that[−2 k+1,2 k+2]^(∗)splits a cyclic group Z m,then m=4 k+2.We prove also that if M=[−k_(1),k_(2)]^(∗)splits Z m purely singularly,and 15≤k_(1)+k_(2)≤30,then m=1,or m=k_(1)+k_(2)+1,or k_(1)=0 and m=2 k_(2)+1.

关 键 词：Splitter sets perfect codes factorizations of cyclic groups 

分 类 号：O157.5[理学—数学]