Concept of Modern Group Theory

International Journal of Mathematics Trends and Technology (IJMTT)
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Mukesh Kumar Choudhary, Dr. S. Biswas


MLA Style: Mukesh Kumar Choudhary, Dr. S. Biswas "Concept of Modern Group Theory" International Journal of Mathematics Trends and Technology 66.12 (2020):79-84. 

APA Style: Mukesh Kumar Choudhary, Dr. S. Biswas(2020). Concept of Modern Group Theory.  International Journal of Mathematics Trends and Technology, 79-84.

In mathematics and abstract algebra, Group theory studies the algebraic structures known as groups. The concept of group is central to abstract algebra. Other well-known algebraic structure, such as rings, fields and vector spaces, can all be seen as groups endowed with additional operations and axioms. Modern group theory an active mathematical discipline-studies groups in their own right. To explore groups, mathematicians have devised various notions to break group into smaller, better understandable pieces, such as subgroups, quotient groups and simple groups.


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Keywords : Group, Abelian-group, Groupoid, Semigroup, Monoid, Finite and Infinite Group, Subgroup and their types, Trivial Subgroup, Symmetry Group, Permutations, Cycles, Cyclic Group, Dihedral Group, Homomorphism of Group, Kernel of Homomorphism, Isomorphism of Group, Coset, Center of Group, Quotient Group, Symmetry.