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@article{189226,
        author = {Manisha Sahu},
        title = {Group Theory in Abstract Algebra: A Comprehensive Study of Structures and Applications},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {12},
        number = {7},
        pages = {5223-5226},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=189226},
        abstract = {Group theory is a fundamental branch of abstract algebra that studies algebraic structures known as groups. It provides a formal framework for understanding symmetry, transformations, and invariance in mathematics and allied sciences. This paper presents a detailed and systematic exposition of group theory, covering its historical background, axiomatic foundations, major classes of groups, subgroup structures, cosets, homomorphisms, quotient groups, and key theorems. Topics such as permutation groups, group actions, direct products, and the Sylow theorems are also discussed in detail. The applications of group theory in physics, chemistry, cryptography, and computer science are highlighted. This work is intended to serve as a comprehensive academic resource for undergraduate and postgraduate students, educators, and researchers.},
        keywords = {},
        month = {December},
        }