Near subgroups of groups Original Research Article

A finite subset A of a group is a near subgroup if the number of ordered pairs (x, y) ϵ A2 with xy ⊂ A is at most /vb A /vb. We show here that if /vb A /vb ⩾ 5, then A is a near subgroup if and only if A ∪ {g} is a subgroup for some group element g. We also classify the counterexamples if /vb A /vb ⩽ 4.