The number of Fuzzy subgroups of some non-abelian groups

Document Type : Research Paper

Authors

1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

2 Department of Pure Mathematics, Ferdowsi University of Mash- had, Mashhad, Iran

Abstract

In this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. Explicit formulas are given
for dihedral groups $D_{2n}$, quasi-dihedral groups $QD_{2^n}$, generalized quaternion groups $Q_{4n}$ and modular $p$-groups $M_{p^n}$.

Keywords


bibitem{ai-hn}A. Iranmanesh and H. Naraghi, {it The connection between some equivalence relations on fuzzy subgroups}, Iranian Journal of Fuzzy Systems, {bf 8(5)} (2011), 69--80.

bibitem{aj}A. Jain, {it Fuzzy subgroups and certain equivalence relations}, Iranian Journal of Fuzzy Systems, {bf 3(2)} (2006), 75--91.

bibitem{rk}R. Kumar, {it Fuzzy Algebra, Vol. I}, University of Delhi, Publication Division, 1993.

bibitem{fl}F. Lazlo, {it Structure and construction of fuzzy subgroup of a group}, Fuzzy Sets and Systems, {bf 51} (1992), 105--109.

bibitem{jnm-krb-ar}J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, {it Fuzzy Group Theory}, Springer, Berlin, 2005.

bibitem{jnm-nk-dsm}J. N. Mordeson, N. Kuroki and D. S. Malik, {it Fuzzy Semigroups}, Springer, Berlin, 2003.

bibitem{vm-bbm-1}V. Murali and B. B. Makamba, {it On an equivalence of fuzzy subgroups I}, Fuzzy Sets and Systems, {bf 123} (2001), 259--264.

bibitem{vm-bbm-2}V. Murali and B. B. Makamba, {it On an equivalence of fuzzy subgroups II}, Fuzzy Sets and Systems, {bf 136} (2003), 93--104.

bibitem{sn-vm-bbm}S. Ngcibi, V. Murali and B. B. Makamba, {it Fuzzy subgroups of rank two abelian $p$-groups}, Iranian Journal of Fuzzy Systems, {bf 7(2)} (2010), 149--153.

bibitem{ar}A. Rosenfeld, {it Fuzzy groups}, J. Math. Anal. Appl., {bf 35} (1971), 512--517.

bibitem{mt-1}M. Tu{a}rnu{a}uceanu, {it The number of fuzzy subgroups of finite
cyclic groups and Delannoy numbers}, European J. Combin., {bf 30} (2009), 283--286.

bibitem{mt-2}M. Tu{a}rnu{a}uceanu, {it Classifying fuzzy subgroups of finite non-abelian groups}, Iranian Journal of Fuzzy Systems, {bf 9(4)} (2012).

bibitem{mt-lb}M. Tu{a}rnu{a}uceanu and L. Bentea, {it On the number of fuzzy subgroups of finite abelian groups}, Fuzzy Sets and Systems, {bf 159} (2008), 1084--1096.

bibitem{acv}A. C. Volf, {it Counting fuzzy subgroups and chains of subgroups}, Fuzzy Syst. Artif. Intell., {bf 10} (2004), 191--200.

bibitem{yz-kz}Y. Zhang and K. Zou, {it A note on an equivalence relation on fuzzy subgroups}, Fuzzy Sets and Systems, {bf 95} (1992), 243--247.