Classifying fuzzy subgroups of the abelian group $\mathbb{Z}_{p_1}\times \mathbb{Z}_{p_2}\times\cdots \times \mathbb{Z}_{p_n}$ for distinct primes $p_1, p_2,\cdots, p_n$
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In this paper, we classify the fuzzy subgroups of the group $G = \mathbb{Z}_{p_1}\times \mathbb{Z}_{p_2}\times\cdots \times \mathbb{Z}_{p_n}$ where $p_1, p_2,\cdots, p_n$ are distinct primes and $n\in \mathbb{Z}^+$. We develop an algorithm for counting the distinct fuzzy subgroups of the group $G$ using the criss-cut counting technique. This is achieved by using the maximal chains of subgroups of $G$ and the equivalence relation given by Murali and Makamba in their research papers on equivalent fuzzy subgroups.
Abstract
In this paper, we classify the fuzzy subgroups of the group $G = \mathbb{Z}_{p_1}\times \mathbb{Z}_{p_2}\times\cdots \times \mathbb{Z}_{p_n}$ where $p_1, p_2,\cdots, p_n$ are distinct primes and $n\in \mathbb{Z}^+$. We develop an algorithm for counting the distinct fuzzy subgroups of the group $G$ using the criss-cut counting technique. This is achieved by using the maximal chains of subgroups of $G$ and the equivalence relation given by Murali and Makamba in their research papers on equivalent fuzzy subgroups.
참고문헌 (17)
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