Linear groups and computation

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed

Linear groups and computation

Funding: A. S. Detinko is supported by a Marie Skłodowska-Curie Individual Fellowship grant (Horizon 2020, EU Framework Programme for Research and Innovation).We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed.PostprintPeer reviewe

Computational Group Theory

This sixth workshop on Computational Group Theory proved that its main themes “finitely presented groups”, “$p$-groups”, “matrix groups” and “representations of groups” are lively and active fields of research. The talks also presented applications to number theory, invariant theory, topology and coding theory

Testing polycyclicity of finitely generated rational matrix groups

We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of GL( d, Q) and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of GL(d, Q).</p

Testing polycyclicity of finitely generated rational matrix groups

Abstract. We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of GL(d, Q) and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of GL(d, Q). 1