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Finitely Presented GroupsIt follows from the well known theorems on the algorithmic unsolvability of the word problem and related problems that there are no deterministic methods to answer most questions about the structure of finitely presented groups. For these essentially two approaches are possible: On one hand trialanderror methods such as the ToddCoxeter and KnuthBendix methods, on the other hand methods to find certain factor groups of described structure, most of which are based on the idea of 'collection'. For theoretical background of the implemented methods see the book [Si94] of Charles Sims. The main GAP library provides methods for handling finitely presented groups such as
Also there are functions to handle Tietze transformations. In addition there are packages
The packages are still (2005) only available through GAP 3. 

The GAP Group Last updated: Wed Dec 21 10:59:43 2016 