counting distinct fuzzy subgroups of some rank-3 abelian groups
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abstract
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.
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Journal title:
iranian journal of fuzzy systemsجلد ۱۴، شماره ۱، صفحات ۱۶۳-۱۸۱
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