{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:17Z","timestamp":1760241617802,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,1]],"date-time":"2018-06-01T00:00:00Z","timestamp":1527811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper we study the neutrosophic triplet groups for    a \u2208  Z  2 p      and prove this collection of triplets    a , n e u t ( a ) , a n t i ( a )    if trivial forms a semigroup under product, and semi-neutrosophic triplets are included in that collection. Otherwise, they form a group under product, and it is of order    ( p \u2212 1 )    , with    ( p + 1 , p + 1 , p + 1 )    as the multiplicative identity. The new notion of pseudo primitive element is introduced in    Z  2 p     analogous to primitive elements in    Z p    , where p is a prime. Open problems based on the pseudo primitive elements are proposed. Here, we restrict our study to    Z  2 p     and take only the usual product modulo    2 p    .<\/jats:p>","DOI":"10.3390\/sym10060194","type":"journal-article","created":{"date-parts":[[2018,6,1]],"date-time":"2018-06-01T03:02:50Z","timestamp":1527822170000},"page":"194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Classical Group of Neutrosophic Triplet Groups Using {Z2p, \u00d7}"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1475","authenticated-orcid":false,"given":"Vasantha Kandasamy","family":"W.B.","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, VIT, Vellore 632014, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4826-9466","authenticated-orcid":false,"given":"Ilanthenral","family":"Kandasamy","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, VIT, Vellore 632014, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","unstructured":"Smarandache, F. (2005). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, American Research Press."},{"key":"ref_4","unstructured":"Vasantha, W.B. (2002). Smarandache Semigroups, American Research Press."},{"key":"ref_5","unstructured":"Vasantha, W.B., and Smarandache, F. (2004). Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models, Hexis."},{"key":"ref_6","unstructured":"Vasantha, W.B., and Smarandache, F. (2005). N-Algebraic Structures and SN-Algebraic Structures, Hexis."},{"key":"ref_7","unstructured":"Vasantha, W.B., and Smarandache, F. (2006). 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Proceedings of the 18th Annual Meeting of the APS Northwest Section, Pacific University, Forest Grove, OR, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"275","DOI":"10.3390\/sym9110275","article-title":"Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups","volume":"9","author":"Zhang","year":"2017","journal-title":"Symmetry"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"126","DOI":"10.3390\/sym10040126","article-title":"Neutrosophic Triplet Cosets and Quotient Groups","volume":"10","author":"Bal","year":"2017","journal-title":"Symmetry"},{"key":"ref_21","unstructured":"Zhang, X.H., Smarandache, F., Ali, M., and Liang, X.L. (2017). Commutative neutrosophic triplet group and neutro-homomorphism basic theorem. Ital. J. Pure Appl. Math., in press."},{"key":"ref_22","unstructured":"Vasantha, W.B., Kandasamy, I., and Smarandache, F. (2017). Neutrosophic Triplet Groups and Their Applications to Mathematical Modelling, EuropaNova."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/6\/194\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:06:45Z","timestamp":1760195205000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/6\/194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,1]]},"references-count":22,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["sym10060194"],"URL":"https:\/\/doi.org\/10.3390\/sym10060194","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,6,1]]}}}