Singular neutrosophic extended triplet groups and generalized groups |
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| Affiliation: | 1. Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China;2. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China;3. Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA;4. Department of Mathematics, Obafemi Awolowo University, Ile Ife 220005, Nigeria;1. Law Department, Beihua University, Jilin Province, China;2. Engineer Department, Yeungnam University, South Korea;1. School of Electronical and Electronics Engineering, Chung-Ang University, 84, Heukseok-Ro, Dongjak-Gu, Seoul 06974, Republic of Korea;2. Korea Institute of Industrial Technology, 143 Hanggaulro, Sangnok-gu, Ansan-si, Gyeonggi-do 15588, Republic of Korea |
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| Abstract: | Neutrosophic extended triplet group (NETG) is an interesting extension of the concept of classical group, which can be used to express general symmetry. This paper further studies the structural characterizations of NETG. First, some examples are given to show that some results in literature are false. Second, the differences between generalized groups and neutrosophic extended triplet groups are investigated in detail. Third, the notion of singular neutrosophic extended triplet group (SNETG) is introduced, and some homomorphism properties are discussed and a Lagrange-like theorem for finite SNETG is proved. Finally, the following important result is proved: a semigroup is a singular neutrosophic extended triplet group (SNETG) if and only if it is a generalized group. |
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| Keywords: | Neutrosophic extended triplet group Generalized group Semigroup Singular neutrosophic extended triplet group Kernel of homomorphism 20N02 20N05 |
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