The Importance of Group Theory in Abstract Algebra

Author(s)	Aniruddha Kumar
Country	India
Abstract	Group theory has emerged as a cornerstone of abstract algebra, providing a unified framework for analyzing symmetrical structures and algebraic operations across diverse mathematical and scientific domains. This paper presents a comprehensive examination of group-theoretic principles, beginning with fundamental axioms and progressing to advanced applications in physics, chemistry, and computer science. We systematically explore key concepts including subgroup formation, homomorphic relationships, and symmetry operations, while highlighting groundbreaking connections to Galois theory and polynomial solvability. The discussion culminates in an analysis of contemporary applications in quantum computing and cryptographic systems, demonstrating group theory's enduring relevance in cutting-edge scientific research.
Keywords	Group theory Abstract algebra Group-theoretic principles Algebraic operations Fundamental axioms
Field	Mathematics
Published In	Volume 16, Issue 2, April-June 2025
Published On	2025-04-24
Cite This	The Importance of Group Theory in Abstract Algebra - Aniruddha Kumar - IJSAT Volume 16, Issue 2, April-June 2025. DOI 10.71097/IJSAT.v16.i2.4064
DOI	https://doi.org/10.71097/IJSAT.v16.i2.4064
Short DOI	https://doi.org/g9gp33

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