2011/02/08 by René Hartung, Hartung, René, Gunnar Traustason +1
Chemistry · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Synthetic Organic Chemistry Methods #math.GR
paper · pdf · doi:10.48550/arxiv.1102.1650
Preprint
openalex publication_date 2011/02/08 · arxiv created 2011/02/09 · arxiv updated 2011/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a new type of polycyclic presentations, that we will call refined solvable presentations, for polycyclic groups. These presentations are obtained by refining a series of normal subgroups with abelian sections. These presentations can be described effectively by presentation maps which yield the basis data structure to define a polycyclic group in computer-algebra-systems like \scshape Gap or \scshape Magma. We study refined solvable presentations and, in particular, we obtain consistency criteria for them. This consistency implementation demonstrates that it is often faster than the existing methods for polycyclic groups.