# Refined solvable presentations for polycyclic groups

Document Type : Research Paper

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Abstract

‎We describe a new type of presentation that‎, ‎when consistent‎, ‎describes a polycyclic group‎. ‎This presentation is obtained by‎ ‎refining a series of normal subgroups with‎ ‎abelian sections‎. ‎These presentations can be described effectively in‎ ‎computer-algebra-systems like $Gap$ or‎ ‎$Magma$‎. ‎We study these‎ ‎presentations and‎, ‎in particular‎, ‎we obtain consistency criteria for them‎. ‎The‎ ‎consistency implementation demonstrates that there are situations where‎ ‎the new method is faster than the‎ ‎existing methods for polycyclic groups‎.

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#### References

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