Abstract
It is shown that for a group G if σμ is a fuzzy subgroup of G for all fuzzy subgroups μ of G × G, then either G is a cyclic group of order pm for some m ≥ 1 or G ∼- Z(p∞), where p is a prime. Conversely, we prove that if either G is a cyclic group of order pm for some m ≥ 1 or G ∼- Z(p∞) then σμ is a fuzzy subgroup of G for any fuzzy subgroup μ, of G × G, where p is a prime.