Fuzzy subgroups of the direct product of a generalized quaternion group and a cyclic group of any odd order
نویسندگان
1 Department of Mathematics, Gangneung-Wonju National University, 7, Jukheon-gil, Gangneung-si, Gangwon-do 210-702, Republic of Korea
doi
10.22111/ijfs.2013.1209چکیده
Bentea and T\u{a}rn\u{a}uceanu~(An. \c{S}tiin\c{t}. Univ. Al. I.Cuza Ia\c{s}, Ser. Nou\v{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$Q_8\times \mathbb{Z}_n$ 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.
