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Oh, Ju-Mok. (1392). An explicit formula for the number of fuzzy subgroups of a finite abelian $p$-group\\ of rank two. نشریه علمی دانشگاه سیستان و بلوچستان, 10(6), 125-135. doi: 10.22111/ijfs.2013.1335
Ju-Mok Oh. "An explicit formula for the number of fuzzy subgroups of a finite abelian $p$-group\\ of rank two". نشریه علمی دانشگاه سیستان و بلوچستان, 10, 6, 1392, 125-135. doi: 10.22111/ijfs.2013.1335
Oh, Ju-Mok. (1392). 'An explicit formula for the number of fuzzy subgroups of a finite abelian $p$-group\\ of rank two', نشریه علمی دانشگاه سیستان و بلوچستان, 10(6), pp. 125-135. doi: 10.22111/ijfs.2013.1335
Oh, Ju-Mok. An explicit formula for the number of fuzzy subgroups of a finite abelian $p$-group\\ of rank two. نشریه علمی دانشگاه سیستان و بلوچستان, 1392; 10(6): 125-135. doi: 10.22111/ijfs.2013.1335

An explicit formula for the number of fuzzy subgroups of a finite abelian $p$-group\\ of rank two

Iranian Journal of Fuzzy Systems
مقاله 11، دوره 10، شماره 6، اسفند 2013، صفحه 125-135    اصل مقاله (397.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2013.1335
نویسنده
Ju-Mok Oh*
Mathematics, Gangneung-Wonju National University, Gangneung, Re- public of Korea
چکیده
Ngcibi, Murali and Makamba [Fuzzy subgroups of rank two abelian
$p$-group, Iranian J. of Fuzzy Systems {\bf 7} (2010), 149-153]
considered the number of fuzzy subgroups of a finite abelian
$p$-group $\mathbb{Z}_{p^m}\times \mathbb{Z}_{p^n}$ of rank two, and
gave explicit formulas for the cases when $m$ is any positive
integer and $n=1,2,3$. Even though their method can be used for the
cases when $n=4,5,\ldots$ by using inductive arguments, it does not
provide an explicit formula for that number  for an arbitrarily
given positive integer $n$. In this paper we give a complete answer
to this problem. Thus for arbitrarily given positive integers $m$
and $n$, an explicit formula for the number of fuzzy subgroups of
$\mathbb{Z}_{p^m}\times \mathbb{Z}_{p^n}$  is given.
کلیدواژه‌ها
Enumeration؛ Fuzzy subgroup؛ Subgroup lattice؛ Abelian $p$-group؛ Schr\"{o}der's triangle
مراجع
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\bibitem{NG05} S. Ngcibi, {\it Studies of equivalent fuzzy
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\bibitem{NMM10} S. Ngcibi, V. Murali and B. B. Makamba, {\em Fuzzy subgroups of rank two
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\bibitem{PS98} E. Pergola and R. A. Sulanke, {\em Schr\"{o}der triangles, paths, and
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