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Standard Generators of Finite Fields and their Cyclic Subgroups

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GRA2 - Groups, representations and applications: new perspectives

This talk will be on the practical problem of generating finitefields for use in, e.g., computer algebra systems or in collections ofmathematical data. I will mention some applications in the representationtheory of groups.Our construction has some nice properties:  it provides standardized generators for finite fields  it includes efficient embeddings of subfields, and allows to compute in   an algebraic closure K of each finite prime field  it provides an explicit and computable embedding from the multiplicative   group of K into the complex roots of unity  it is easy to implement and efficient in practiceSo far, Conway polynomials were used in various software packages and formodular character tables of finite groups. But these are difficult to compute,and our construction can be used as an alternative.

This talk is part of the Isaac Newton Institute Seminar Series series.

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