The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence G (I), X1, X2, … is the identity, then G (I) is nilpotent.
The objective of this paper is to study some of AH-substructures in n-refined neutrosophic group. Also, it deals with some elementary properties of AH-subgroups, AH-normality, AH-homomorphisms, and endomorphisms especially in a non abelian n-refined neutrosophic group.
After introducing the notion of hyperstructures about 80 years ago by F. Marty, a number of researches on its theory, generalization, and it’s applications have been done. On the other hand, the theory of Neutrosophy, the study of neutralities, was developed in 1995 by F. Smarandache as an extension of dialectics. This paper aims at finding a connection between refined neutrosophy of sets and hypergroups. In this regard, we define refined neutrosophic quadruple hypergroups, study their properties, and find their fundamental refined neutrosophic quadruple groups. Moreover, some results related to refined neutrosophic quadruple po-hypergroups are obtained.
A well known and referenced global result is the nilpotent characterisation of the finite p-groups. This un doubtedly transends into neutrosophy. Hence, this fact of the neutrosophic nilpotent p-groups is worth critical studying and comprehensive analysis. The nilpotent characterisation depicts that there exists a derived series (Lower Central) which must terminate at {ϵ} ( an identity ), after a finite number of steps. Now, Suppose that G(I) is a neutrosophic p-group of class at least m ≥ 3. We show in this paper that Lm−1(G(I)) is abelian and hence G(I) possesses a characteristic abelian neutrosophic subgroup which is not supposed to be contained in Z(G(I)). Furthermore, If L3(G(I)) = 1 such that pm is the highest order of an element of G(I)/L2(G(I)) (where G(I) is any neutrosophic p-group) then no element of L2(G(I)) has an order higher than pm.
This paper is the continuation of the work started in the paper titled “Refined Neutrosophic Rings I”. In the present paper, we study refined neutrosophic ideals and refined neutrosophic homomorphisms along their elementary properties.
In this paper, one extends the single-valued complex neutrosophic set to the subset-valued complex neutrosophic set, and afterwards to the subset-valued complex refined neutrosophic set.
[ADDRESSED CITATION] [HG206b] Henry Garrett, “Dual Domination In Neutrosophic SuperHyperGraphs 6”. Dr. Henry Garrett, 2024 (doi: 10.5281/zenodo.12651785). In this scientific research book, there are some scientific research chapters on “Extreme Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs” and “Neutrosophic Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs” about some scientific researches on Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs and Neutrosophic Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs. With scientific research on the basic scientific research properties, the scientific research book starts to make Extreme Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs theory and Neutrosophic Connected Perfect Dual Domination In Neutrosophic SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4048 readers in Scribd. It’s titled “Beyond Neutrosophic Graphs” and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 5046 readers in Scribd. It’s titled “Neutrosophic Duality” and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating In Neutrosophic SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It’s smart to consider a set but acting on its complement that what’s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). “Neutrosophic Duality”, Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf).
[ADDRESSED CITATION] [HG195b] Henry Garrett, “Dominating Sequence In Neutrosophic SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.10042973). In this scientific research book, there are some scientific research chapters on “Extreme Dominating Sequence In Neutrosophic SuperHyperGraphs” and “Neutrosophic Dominating Sequence In Neutrosophic SuperHyperGraphs” about some scientific researches on Dominating Sequence In Neutrosophic SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme Dominating Sequence In Neutrosophic SuperHyperGraphs and Neutrosophic Dominating Sequence In Neutrosophic SuperHyperGraphs. With scientific research on the basic scientific research properties, the scientific research book starts to make Extreme Dominating Sequence In Neutrosophic SuperHyperGraphs theory and Neutrosophic Dominating Sequence In Neutrosophic SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It’s titled “Beyond Neutrosophic Graphs” and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It’s titled “Neutrosophic Duality” and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperPerfect Search In SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It’s smart to consider a set but acting on its complement that what’s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). “Neutrosophic Duality”, Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). — — — 316 [HG316] Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph With Multipartite and Cycle By Dominating Sequence As Hyper Decoration On Super Density”, Zenodo 2023, (doi: 10.5281/zenodo.10263440). @ResearchGate: https://www.researchgate.net/publication/376230123 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/10263440 @academia: https://www.academia.edu/110646753 — 316 [HG316] Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph With Multipartite and Cycle By Dominating Sequence As Hyper Decoration On Super Density”, Zenodo 2023, (doi: 10.5281/zenodo.10263440). @facebook: https://www.facebook.com/DrHenryGarrettNYC/posts/pfbid05MKoSp68f2E63VCLKZKjA49j9sMABTeRVSLwV4MxsT5qK6gZDo8ctEmhngEo1q86l PAGE @facebook: https://www.facebook.com/DrHenryGarrett/posts/pfbid036P7TpAMYVdbAMnLbKKssrbfeetMd7DmWXPEmSbfCup7qbx5TNmiR29KRZTZyDidl @LinkedIn: https://www.linkedin.com/feed/update/urn:li:ugcPost:7137860793093529600/ @instagram: https://www.instagram.com/p/C0ewc4iLT4A/ @X: https://x.com/DrHenryGarrettX/status/1732094549369999857?s=20 @X: https://x.com/DrHenryGarrettX/status/1732094791800721866?s=20 @X: https://x.com/DrHenryGarrettX/status/1732094837304786944?s=20 — — 317 [HG317] Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph With Bipartite and Path By Dominating Sequence As Hyper Decoration On Super Density”, Zenodo 2023, (doi: 10.5281/zenodo.10299535). @ResearchGate: https://www.researchgate.net/publication/376314727 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/10299535 @academia: https://www.academia.edu/110872281 — 317 [HG317] Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph With Bipartite and Path By Dominating Sequence As Hyper Decoration On Super Density”, Zenodo 2023, (doi: 10.5281/zenodo.10299535). @facebook: https://www.facebook.com/DrHenryGarrettNYC/posts/pfbid036a6EZhMmNnMA8N1VNhygQfxShxw5SXfTAxBPFin4VKUUq7i7xQn5AJMhSQBVaYDfl PAGE @facebook: https://www.facebook.com/DrHenryGarrett/posts/pfbid0r7Mk6Rtnw19SmJvkvrdXsE3P1ZCXxgr87CTpkKHdyWjsNCCG2b37xPQwUafoRbf1l @LinkedIn: https://www.linkedin.com/feed/update/urn:li:ugcPost:7138824505182842881/ @Instagram: https://www.instagram.com/p/C0lmWzAKsUr/ @Twitter: https://x.com/DrHenryGarrettX/status/1733058108413366361?s=20 @Twitter: https://x.com/DrHenryGarrettX/status/1733058088381399323?s=20 @Twitter: https://x.com/DrHenryGarrettX/status/1733058015232741605?s=20 — — 318 [HG318] Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph With Star and Wheel By Dominating Sequence As Hyper Decoration On Super Density”, Zenodo 2023, (doi: 10.5281/zenodo.10371529). @ResearchGate: https://www.researchgate.net/publication/376477572 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/10371529 @academia: https://www.academia.edu/111329570 — 318 [HG318] Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph With Star and Wheel By Dominating Sequence As Hyper Decoration On Super Density”, Zenodo 2023, (doi: 10.5281/zenodo.10371529). @facebook: https://www.facebook.com/DrHenryGarrettNYC/posts/pfbid02vVPDwjGKSduiP19fRrVfCbKYx28XWsdA9tZwbexd3EnG1CiW4Vk1xFeBfEnjroMjl PAGE @facebook: https://www.facebook.com/DrHenryGarrett/posts/pfbid02eHrDgBHCgH1G887Y9Hp37ZS2oXCW8me5b4gvedDn8Ew7z8JMy4Vm3unVX3GchNuUl @LinkedIn: https://www.linkedin.com/feed/update/urn:li:activity:7140980225345069056 @Instagram: https://www.instagram.com/p/C00616YMjnn/ @Twitter: https://x.com/DrHenryGarrettX/status/1735212500545650728?t=E9MfGi4pqOnpEE1FHUE9fg\&s=19 @Twitter: https://x.com/DrHenryGarrettX/status/1735213214353265094?t=UI\_LOXibEQRI3DR39nkanQ\&s=19 @Twitter: https://x.com/DrHenryGarrettX/status/1735213998692274638?t=t4DV1z7AdP6-L-M1u9aWFw\&s=19 — “Book #195” [ADDRESSED CITATION] [HG195b] Henry Garrett, “Dominating Sequence In Neutrosophic SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.10042973). @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/- @WordPress: https://drhenrygarrett.wordpress.com/2023/12/17/Dominating-Sequence-In-Neutrosophic-SuperHyperGraphs/ @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/10042973 @academia:https://www.academia.edu/- Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle — — [HG195b] Henry Garrett, “Dominating Sequence In Neutrosophic SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.10042973). #Link (KE):https://www.amazon.com/dp/- (SC):https://www.amazon.com/dp/- (HC):https://www.amazon.com/dp/- #ISBN CC BY-NC-ND 4.0 - - Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle — -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle —
[ADDRESSED CITATION] [HG208b] Henry Garrett, “Burning Number In Neutrosophic SuperHyperGraphs”. Dr. Henry Garrett, 2024 (doi: 10.5281/zenodo.12797511). In this scientific research book, there are some scientific research chapters on “Extreme Burning Number In Neutrosophic SuperHyperGraphs” and “Neutrosophic Burning Number In Neutrosophic SuperHyperGraphs” about some scientific researches on Burning Number In Neutrosophic SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme Burning Number In Neutrosophic SuperHyperGraphs and Neutrosophic Burning Number In Neutrosophic SuperHyperGraphs. With scientific research on the basic scientific research properties, the scientific research book starts to make Extreme Burning Number In Neutrosophic SuperHyperGraphs theory and Neutrosophic Burning Number In Neutrosophic SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4048 readers in Scribd. It’s titled “Beyond Neutrosophic Graphs” and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 5046 readers in Scribd. It’s titled “Neutrosophic Duality” and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating In Neutrosophic SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It’s smart to consider a set but acting on its complement that what’s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). “Neutrosophic Duality”, Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). “SCIENTIFIC RESEARCH BOOK #208” [ADDRESSED CITATION] [HG208b] Henry Garrett, “Burning Number In Neutrosophic SuperHyperGraphs”. Dr. Henry Garrett, 2024 (doi: 10.5281/zenodo.12797511). @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/382882738 @WordPress: https://drhenrygarrett.wordpress.com/2024/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/12797511 @academia:https://www.academia.edu/122609889 Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @X @facebook @LinkedIn @Instagram @YouTube @Amazon @googlebooks @GooglePlay @AmazonKindle
The study of refined neutrosophic rings is the objective of this paper. Substructures of refined neutrosophic rings and their elementary properties are presented. It is shown that every refined neutrosophic ring is a ring.
