24 Words in Finite Polycyclic Groups

Ag words are the GAP datatype for elements of finite polycyclic groups. Unlike permutations, which are all considered to be elements of one large symmetric group, each ag word belongs to a specified group. Only ag words of the same finite polycyclic group can be multiplied.

The following sections describe ag words and their parent groups (see Ag Word Comparisons), functions for ag words and some low level functions for ag words (starting at CentralWeight and CanonicalAgWord).

For operations and functions defined for group elements in general see Comparisons of Group Elements, Operations for Group Elements.

Subsections

  1. More about Ag Words
  2. Ag Word Comparisons
  3. CentralWeight
  4. CompositionLength
  5. Depth
  6. IsAgWord
  7. LeadingExponent
  8. RelativeOrder
  9. CanonicalAgWord
  10. DifferenceAgWord
  11. ReducedAgWord
  12. SiftedAgWord
  13. SumAgWord
  14. ExponentAgWord
  15. ExponentsAgWord
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GAP 3.4.4
April 1997