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COUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 ABELIAN GROUPS | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 12، دوره 14، شماره 1، اردیبهشت 2017، صفحه 163-181 اصل مقاله (380.56 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3051 | ||
نویسندگان | ||
Isaac K. Appiah؛ B. B. Makamba ![]() | ||
Department of Mathematics, University of Fort Hare, ALICE, 5700, South Africa | ||
چکیده | ||
In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = \mathbb{Z}_{p^n} + \mathbb{Z}_p + \mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in \cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorphic maximal chains of subgroups and (v) classes of isomorphic fuzzy subgroups of $G$. Illustrative examples are provided. | ||
کلیدواژهها | ||
Equivalence؛ Fuzzy subgroup؛ Maximal chain؛ Keychain؛ Distinguishing factor؛ Isomorphism | ||
مراجع | ||
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