Assmann, Björn; Eick, Bettina Computing polycyclic presentations for polycyclic rational matrix groups. (English) Zbl 1124.20306 J. Symb. Comput. 40, No. 6, 1269-1284 (2005). Summary: We describe practical algorithms for computing a polycyclic presentation and for facilitating a membership test for a polycyclic subgroup of \(\text{GL}(d,\mathbb{Q})\). A variation of this method can be used to check whether a finitely generated subgroup of \(\text{GL}(d,\mathbb{Q})\) is solvable or solvable-by-finite. We report on our implementations of the algorithms for determining a polycyclic presentation and checking solvability. Cited in 1 ReviewCited in 12 Documents MSC: 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 20F16 Solvable groups, supersolvable groups 20F05 Generators, relations, and presentations of groups 20-04 Software, source code, etc. for problems pertaining to group theory 68W30 Symbolic computation and algebraic computation 20E07 Subgroup theorems; subgroup growth 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) Keywords:polycyclic groups; polycyclic presentations; matrix groups; finitely generated groups; general linear groups; algorithms; membership tests; finitely generated subgroups; solvable-by-finite subgroups Software:AClib; GAP; ALNUTH; Polycyclic; Polenta; KANT/KASH PDFBibTeX XMLCite \textit{B. Assmann} and \textit{B. Eick}, J. Symb. Comput. 40, No. 6, 1269--1284 (2005; Zbl 1124.20306) Full Text: DOI References: [1] Assmann, B., 2003a. Polenta—Polycyclic presentations for matrix groups. 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