The Classification of Finite Simple Groups is a monumental achievement in mathematics, providing a comprehensive list of all possible finite simple groups, which are the building blocks of all finite groups. This classification includes 18 infinite families and 26 sporadic groups, and its proof spans thousands of pages contributed by numerous mathematicians over several decades.

Classification Of Finite Simple Groups

Monumental achievement in mathematics

Comprehensive list of all possible finite simple groups

Building blocks of all finite groups

Infinite families

Sporadic groups are a set of 26 exceptional groups in the classification of finite simple groups, which do not fit into any of the infinite families of simple groups. They are important in group theory for their role in the Monster group, which is the largest sporadic group and has connections to various areas of mathematics, including number theory and geometry.

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