Abstract
special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity We describe an algorithm to compute tensor decompositions of central products of groups. The novelty over previous algorithms is that in the case of matrix groups that are both tensor decomposable and imprimitive, the new algorithm more often outputs the more desirable tensor decomposition.
Highlights
A recent active area of computational group theory is the so-called matrix group recognition project
Babai and Beals define a series of characteristic subgroups, present in all finite groups, and initiate a program that tries to compute a composition series going through these characteristic subgroups
The present paper is a contribution to the growing library of algorithms for the geometric approach, in the case of tensor product groups
Summary
A recent active area of computational group theory is the so-called matrix group recognition project. The black-box group approach of Babai and Beals [2] aims for the abstract group theoretic structure of G. The original aim of the black-box group approach was the development of an algorithm with fast asymptotic running time. This aim was recently achieved in [3]. The primary goal of the geometric approach is the development of a practical algorithm for matrix group recognition. The original aim of the geometric approach was the development of a practical algorithm and the guiding principle of the black-box group approach was a rigorous complexity analysis, recent developments combine the two aims very successfully. The present paper is a contribution to the growing library of algorithms for the geometric approach, in the case of tensor product groups
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