Computational group theory

In mathematics, computational group theory is the study of

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groups by means of computers. It is concerned

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with designing and analysing algorithms and

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data structures to compute information about groups. The subject

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has attracted interest because for many interesting groups

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(including most of the sporadic groups) it is impractical

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to perform calculations by hand.

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Important algorithms in computational group theory include:

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• the Schreier-Sims algorithm for finding the order of a permutation group
• the Todd-Coxeter algorithm and Knuth-Bendix algorithm for coset enumeration
• the product-replacement algorithm for finding random elements of a group

Two important computer algebra systems (CAS) used for group theory are

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GAP and MAGMA. Historically, other systems such as CAS (for character theory) and CAYLEY (a predecessor of MAGMA) were important.

Related Topics:
GAP - MAGMA - Character theory - CAYLEY

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Some achievements of the field include:

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• complete enumeration of all finite groups of order less than 2000
• computation of representations for all the sporadic groups
 
Computational group theory: Computational Group Theory References ►