supported in part by the Fundamental Research Funds for the Central Universities(No.3122019152);the National Natural Science Foundation of China(Grant Nos.11701256,11871258);the Youth Backbone Teacher Foundation of Henan's University(No.2019GGJS196);the China Scholarship Council(Grant No.201908410132);was also supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN 2017-03903).
Let G be a finite abelian group and S be a sequence with elements of G.We say that S is a regular sequence over G if|SH|≤|H|-1 holds for every proper subgroup H of G,where SH denotes the subsequence of S consisting o...