Counting of the distinct fuzzy subgroups of the dihedral group D2p n

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dc.contributor.authorNaraghi, Hassan
dc.date.accessioned2024-07-12T20:49:50Z
dc.date.available2024-07-12T20:49:50Z
dc.date.issued2009en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractIn this paper, by using of an equivalence relation on fuzzy subgroup, we determine the number of distinct fuzzy subgroups of the dihedral group of order 2p n such that p is a prime and p ? 3. A fuzzy subset of a set X is mapping µ : X ? [0, 1]. Fuzzy subset µ of a group G is called a fuzzy subgroup of G if (G1) µ(xy) ? µ(x) ? µ(y)?x, y ? G; (G2) µ(x ?1 ) ? µ(x)?x ? G. The set of all fuzzy subgroup of a group G denoted by F (G). Let G be a group, and µ, ? ? F (G). Defined three equivalence relation as follow respectively: (i) We say that µ is equivalence ?, written as µ ? ? if Fµ = F? . (ii) We say that µ is equivalent to ?, written as µ ? ? if 1. µ(x) > µ(y) ? ?(x) > ?(y), for all x, y ? G. 2. µ(x) = 0 ? ?(x) = 0, for all x ? G. (iii) We say that µ is equivalence ?, written as µ 't ? if there exists an isomorphism f from suppµ to supp? such that for all x, y ? suppµ, µ(x) > µ(y) ? ?(f(x)) > ?(f(y)) Let G be a group and µ, ? ? F (G). We say that µ is equivalence ?, written as µ ?t ?, if and only if Fµ = F? and suppµ = supp?. The set of all fuzzy subgroups µ of G such that µ(e) = 1 denoted by F1(G) . The number of equivalence classes ? on F1(G) will be denoted by r ? G. Theorem. Suppose that p be a prime and p ? 3. If G is a dihedral group of order 2p n, then r ? G = nP?1 i=1 p i r ? (D2pn?i ) + pn?p p?1 + 2n+2 + 4p n ? 1.en_US
dc.identifier.citationNaraghi, H. (2009). Counting of the distinct fuzzy subgroups of the dihedral group D2p n. Maltepe Üniversitesi. s. 192.en_US
dc.identifier.endpage193en_US
dc.identifier.isbn9.78605E+12
dc.identifier.startpage192en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2242
dc.institutionauthorNaraghi, Hassan
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07569
dc.titleCounting of the distinct fuzzy subgroups of the dihedral group D2p nen_US
dc.typeConference Object
dspace.entity.typePublication

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