Concept of Modern Group Theory

Mukesh Kumar Choudhary; Dr. S. Biswas

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P512

Concept of Modern Group Theory

Mukesh Kumar Choudhary, Dr. S. Biswas

Abstract

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.

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.

References

[1] ISRAEL KLEINER, “The Evolution of Group Theory A Brief Survey” (York University North York, Ontario Canada M3J1P3 VOL 59 NO 4 OCTOBER 1986)
[2] Ferdi Arya Setiawan, “Group Theory” Dept of Theoretical physics university of Lund, Solvegatan 14A,223 62 Lund-Sweden
[3] Alistar Savage, “Modern Group Theory” Dept of Mathematics and Statistics university of Ottawa.
[4] Smith, David Eugene “History of Modern Mathematics” (1906), Mathematical Monographs,
[5] Debabrata Basu , “Introduction to Classical and Modern Analysis and Their Application to Group Representation Theory” (Indian Institute of Technology, India)
[6] Wussing, Hans, “The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory” (2007)
[7] Judson, Thomas W., “Abstract Algebra: Theory and Applications” (1997)
[8] La Harpe, Pierre de, “Topics in geometric group theory” (2000) University of Chicago Press
[9] Scott, W. R. “Group Theory” (1987) [1964], Inexpensive and fairly readable, but somewhat dated in emphasis, style, and notation
[10] Rotman, Joseph, “An introduction to the theory of groups” (1994)

Citation :

Mukesh Kumar Choudhary, Dr. S. Biswas, "Concept of Modern Group Theory," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 79-84, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P512