【摘要】 假若G=Z_m1（?）Z_m2（?）…_?Z_mr为（m₁,m₂,…,m_r）型Abelian群,其中Z_mi为m_i阶的循环群且1≤i≤r,m₁|m₂|…|m_r,S为G的满足0∈S=-S的生成子集.如果|S|>|G|/ρ,其中ρ≥[m_r/2]且m_r=e（G）为群G的所有元素的阶的最小公倍数,则ρS=G.更进一步作者推广了Klopsch与lev的一个结论,有:若G=Z₂（?）Z_m为（2,m）型Abelian群（m≥8）,则t_m/2（G）=0.更多还原

【Abstract】 Suppose G = Z_m1⊕Z_m2⊕…⊕Z_mr be an Abelian group of type（m₁,m₂,...,m_r） （Z_mi is a cyclic group of order m_i,1≤i≤r,m₁|m₂|…|m_r）.Let S be a symmetrically closed set（S is symmetrically closed if 0∈S = -S） and a generating set of G.If |S|>|G|/p,where p≥[m_r/2]and m_r = e（G） denotes the least common multiple of the orders of all elements of group G,then pS = G.And if G = Z₂⊕Z_m is an Abelian group of type（2,m）（m≥8）,then t_m/2（G） = 0,which extends the related results of Klopsch and Lev.更多还原