An extremal problem on group connectivity of graphs

Let AA be an Abelian group, n≥3n≥3 be an integer, and ex(n,A)ex(n,A) be the maximum integer such that every nn-vertex simple graph with at most ex(n,A)ex(n,A) edges is not AA-connected. In this paper, we study ex(n,A)ex(n,A) for |A|≥3|A|≥3 and present lower and upper bounds for 3≤|A|≤43≤|A|≤4 and an upper bound for |A|≥5|A|≥5.