Visualizing the Group Homomorphism Theorem

1995 ◽  
Vol 26 (2) ◽  
pp. 143
Author(s):  
Robert C. Moore
Keyword(s):  
Group Homomorphism ◽  
Homomorphism Theorem

Generalising and dualising the third list-homomorphism theorem

2011 ◽  
Vol 46 (9) ◽  
pp. 385-391
Author(s):  
Shin-Cheng Mu ◽  
Akimasa Morihata
Keyword(s):  
The Third ◽  
Homomorphism Theorem

scholarly journals Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 321 ◽  
Author(s):  
Mehmet Çelik ◽  
Moges Shalla ◽  
Necati Olgun
Keyword(s):  
Group Theory ◽  
Significant Role ◽  
Classical Group ◽  
Algebraic Structures ◽  
Algebraic Systems ◽  
Homomorphism Theorem ◽  
Special Cases ◽  
Isomorphism Theorems

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

scholarly journals Twisted Alexander polynomials and surjectivity of a group homomorphism

2005 ◽  
Vol 5 (4) ◽  
pp. 1315-1324 ◽  
Author(s):  
Teruaki Kitano ◽  
Masaaki Suzuki ◽  
Masaaki Wada
Keyword(s):  
Group Homomorphism ◽  
Alexander Polynomials

Extensions of I-Bisimple Semigroups

1967 ◽  
Vol 19 ◽  
pp. 419-426 ◽  
Author(s):  
R. J. Warne
Keyword(s):  
Homomorphic Image ◽  
Natural Order ◽  
Isomorphism Theorem ◽  
Maximal Group ◽  
Homomorphism Theorem ◽  
Complete Determination ◽  
Explicit Determination ◽  
Usual Order

A bisimple semigroup S is called I-bisimple if Es, the set of idempotents of S, with its natural order is order-isomorphic to I, the set of integers, under the reverse of the usual order. In (9), the author completely determined the structure of I-bisimple semigroups mod groups; in this paper, he also gave an isomorphism theorem, a homomorphism theorem, an explicit determination of the maximal group homomorphic image, and a complete determination of the congruences for these semigroups.

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