A NOVEL ALGORITHMIC FRAMEWORK FOR CLASSIFICATION OF FINITE SIMPLE GROUPS
DOI:
https://doi.org/10.60787/tnamp.v23.620Keywords:
Finite simple groups, Group classification, Computational group theory, Sylow theorems, Algorithmic simplicity testingAbstract
The classification of finite simple groups (CFSG) is a cornerstone of group theory, categorizing these fundamental algebraic structures into four families: cyclic groups of prime order, alternating groups, Lie-type groups, and sporadic groups. This paper presents a novel algorithmic framework for identifying and classifying finite simple groups within a specified order range (up to 10,000). The algorithm integrates Sylow theorems, a specific divisibility condition for efficiency, and computational group theory techniques to systematically determine simplicity and classify groups into their respective categories. The paper offers a computationally optimized approach for group classification, with potential applications in cryptography, coding theory, and computational algebra.
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