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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

The construction of fuzzy subgroups of groups with units modulo 20 and 21

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pp. 1619–1625Vol. 27Issue 5August 2024DOI: 10.47974/JDMSC-2004 Crossmark XML
Received:
09 Jan 2024
Published Online:
26 Aug 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2004
Pages:
1619–1625

Abstract

The number of fuzzy subgroups (NFSGs) of the groups of units U20 and U21  are determining in this study. The (NFSGs) of U20 was found based on diagram and using the lemma which state that the (NFSGs) of G is equal to the number of chains (NC) on the subgroups lattice of G. Moreover, we explain that there are only two fuzzy subgroups for a prime order group. Lagrange’s theorem is more important in this work, from Lagrange’s theorem, there is no nontrivial subgroup of U21 since the order of the group is prime. We prove that, if P1 (μ) = U21, then we get μ1(x) = θ1, ∀x ∈ U21. Thus we have one fuzzy subgroup of  P1 (μ) = U21. If P1 (μ) = {1}, then we obtain μ2(x) = θ1, ∀x ∈ {1} and μ2 (x) = θ2,∀x∈U21\{1}. Thus we have 2 fuzzy subgroups of U21. We came up with the numbers 21 and 2 respectively.

Keywords

Lagrange theoremSylow theoremSylow subgroupSylow p-subgroupFuzzy subgroupLatticeModuloFuzzy number

Subject Classifications

Primary 13A02Secondary 16W50

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