h1

TY  - THES
AU  - Rademacher, Daniel
TI  - Constructive recognition of finite classical groups with stingray elements
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2024-09688
SP  - 1 Online-Ressource : Illustrationen
PY  - 2024
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
N1  - Dissertation, RWTH Aachen University, 2024
AB  - 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.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2024-09688
UR  - https://publications.rwth-aachen.de/record/995067
ER  -