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arXiv · 1005.0548

Finding direct product decompositions in polynomial time

James B. Wilson
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Abstract

A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indecomposable subgroups. The process uses bilinear maps and commutative rings to characterize direct products of p-groups of class 2 and reduces general groups to p-groups using group varieties. The methods apply to quotients of permutation groups and operator groups as well.

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James B. Wilson. 2010-05-04. Finding direct product decompositions in polynomial time. https://doi.org/10.1515/gcc-2012-0007

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