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SUMMARY:Standard Generators of Finite Fields and their Cyclic Subgroups - 
 Frank Lübeck (RWTH Aachen University)
DTSTART:20220614T101500Z
DTEND:20220614T111500Z
UID:TALK175406@talks.cam.ac.uk
DESCRIPTION:This talk will be on the practical problem of generating finit
 efields for use in\, e.g.\, computer algebra systems or in collections ofm
 athematical data. I will mention some applications in the representationth
 eory of groups.Our construction has some nice properties:&nbsp\;- it provi
 des standardized generators for finite fields&nbsp\;- it includes efficien
 t embeddings of subfields\, and allows to compute in&nbsp\;&nbsp\; an alge
 braic closure K of each finite prime field&nbsp\;- it provides an explicit
  and computable embedding from the multiplicative&nbsp\;&nbsp\; group of K
  into the complex roots of unity&nbsp\;- it is easy to implement and effic
 ient in practiceSo far\, Conway polynomials were used in various software 
 packages and formodular character tables of finite groups. But these are d
 ifficult to compute\,and our construction can be used as an alternative.
LOCATION:Seminar Room 2\, Newton Institute
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