fuzzy subgroups of the direct product of a generalized quaternion group and a cyclic group of any odd order

bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general group: the direct product of a generalizedquaternion group of any even order and a cyclic group of any oddorder. for this group we give an explicit formula for the number offuzzy subgroups.