Estimation and computation with matrices over finite fields

Brian Corr

    Research output: ThesisDoctoral Thesis

    632 Downloads (Pure)

    Abstract

    [Truncated abstract] The Matrix Group Recognition Project is a worldwide effort to produce efficient algorithms for working with arbitrary matrix groups over finite fields. Such groups are potentially very large in comparison to the input length, and dealing with them using deterministic methods is impractical. When a generating set for a group is input into a computer, a constructive recognition algorithm names the group, and nds an e cient mapping between the input generators and a set of 'standard generators', which allow various important questions to be answered quickly. Constructive recognition is a major, natural goal in computational group theory. To recognise an arbitrary group, there are two tasks to perform: the first is to decompose the group into smaller components if possible, and work recursively. The second is to deal with irreducible cases, which in this case are the Finite Simple Groups...
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2014

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