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

Document Type: Research Paper

Author

Department of Mathematics, Gangneung-Wonju National University, 7, Jukheon-gil, Gangneung-si, Gangwon-do 210-702, Republic of Korea

Abstract

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 the
number of fuzzy subgroups of a finite hamiltonian group of type
$Q_8\times \mathbb{Z}_n$ where $Q_8$ is the quaternion group of
order $8$ and $n$ is an arbitrary odd integer. In this paper we
consider more general group: the direct product of a generalized
quaternion group of any even order and a cyclic group of any odd
order. For this group we give an explicit formula for the number of
fuzzy subgroups.

Keywords


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