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@PHDTHESIS{Rademacher:995067,
      author       = {Rademacher, Daniel},
      othercontributors = {Niemeyer, Alice Catherine and Horn, Max and Praeger, Cheryl
                          E.},
      title        = {{C}onstructive recognition of finite classical groups with
                      stingray elements},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2024-09688},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2024},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2024},
      abstract     = {In 1988 Joachim Neubüser posed a matrix group related
                      question in Oberwolfach which was answered by Peter Neumann
                      and Cheryl E. Praeger in 1992. This initiated an
                      international research effort, the matrix group recognition
                      project, within the area of computational group theory with
                      the aim of answering fundamental questions about arbitrary
                      matrix groups over finite fields. One possible method is a
                      data structure called composition tree. In this approach,
                      computations of a large matrix group are decomposed into
                      computations for smaller matrix groups until this process
                      cannot be repeated anymore. The remaining leaf groups are
                      the finite (quasi-)simple groups, which include the
                      classical groups. Therefore, efficient algorithms to deal
                      with classical groups are essential for the overall
                      performance of the composition tree. One elementary aim is
                      to develop an efficient algorithm for the constructive
                      recognition of these groups. This thesis presents a novel
                      algorithm for constructively recognising classical groups
                      within their natural representations, building upon
                      preliminary concepts from Ákos Seress and Max Neunhöffer
                      for special linear groups. The algorithm consists of three
                      subalgorithms: GoingDown algorithm: Recursively descends
                      from the input group $G$ to a subgroup $U$ isomorphic to a
                      "base case group'' using stingray duos and reaching such a
                      group in significantly fewer steps than traditional methods.
                      BaseCase algorithm: Utilises an efficient method for
                      constructively recognising the base case group $U$ forming a
                      starting point for the computation of standard generators of
                      $G$. GoingUp Algorithm: Extends standard generators from the
                      subgroup $U$ to the original group $G$, employing an
                      original approach to compute generators for intermediate
                      subgroups. This research contributes to the broader goal of
                      enhancing computational methods for matrix group
                      recognition, with a particular focus on classical groups. It
                      presents efficient algorithms that improve the performance
                      of the composition tree method.},
      cin          = {115320 / 114410 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)115320_20140620$ / $I:(DE-82)114410_20140620$ /
                      $I:(DE-82)110000_20140620$},
      pnm          = {DFG project G:(GEPRIS)453084359 - Berechnungen mit
                      Matrixgruppen (B07) (453084359) / TRR 195: Symbolische
                      Werkzeuge in der Mathematik und ihre Anwendung (286237555)},
      pid          = {G:(GEPRIS)453084359 / G:(GEPRIS)286237555},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2024-09688},
      url          = {https://publications.rwth-aachen.de/record/995067},
}