Group Connectivity in 3-Edge-Connected Graphs

Let A be an abelian group with |A|?≥ 4. For integers k and l with k?>?0 and l?≥ 0, let ${{mathcal C}(k, l)}$ denote the family of 2-edge-connected graphs G such that for each edge cut ${Ssubseteq E(G)}$ with two or three edges, each component of G ? S has at least (|V(G)| ? l)/k vertices. In this paper, we show that if G is 3-edge-connected and ${Gin {mathcal C}(6,5)}$ , then G is not A-connected if and only if G can be A-reduced to the Petersen graph.