Solvable residues, involutions and related reduction algorithm analyses of maximal subgroups of symplectic type groups

Computational Algebra, particularly within the field of Computational Group Theory (CGT), Focuses on developing algorithmic methods to anayze the structure of classical groups. One of the major research topics in this area is the design of reduction (homomorphism) algorithms for the maximal subgroups of classical groups classified under the Ascbacher framework and the detailed analyses of these algorithms. This study extends previous analyses of the BlindDescend algorithm conducted for the case d=r,d=r^2,〖d=r〗^3 within the Ascbacher class C_6. Here, the cases d=r^4,d=r^5 "," 〖d=r〗^6 are examined without any additional assumptions. The analyses are carried out on the symplectic groups Sp(8,r),Sp(10,r),Sp(12,r). During the analysis, the solvable residuals of the maximal subgroups, the perfect subgroups of these residuals and the involutions contained within these groups have been thoroughly investigated. The obtained results demonstrate that the BlindDescent algorithm can be effectively applied to higer dimensional classical groups even in the absence of additional structural constraints. This thesis has been supported by Tubitak under the project number 121F477.