construct a composition series of a finite group
compute the composition length of a group
CompositionSeries( G )
CompositionLength( G )
a permutation group
A composition series of a group G is a subnormal series
of G, for which each term is a maximal normal subgroup in the preceding term, so that the successive quotients GkGk+1 are simple groups.
Every finite group has a composition series, and any two composition series for a finite group have the same number of terms, and the multi-set of isomorphism types of the quotients GkGk+1 is unique (apart from order). The number r of terms in a composition series is therefore independent of the chosen series, and so the composition length, r−1 of the group G is well-defined.
The CompositionSeries( G ) command constructs a composition series of a finite group G. The group G must be an instance of a permutation group. The returned composition series of G is represented by a series data structure which admits certain operations common to all series. See GroupTheory[Series].
The CompositionLength( G ) command returns the composition length of G; that is, the length of a composition series of G. This is the number of subgroup inclusions - so it is one less than the number of groups in the derived series.
G≔ < a permutation group on 9 letters with 7 generators >
cs≔ < a permutation group on 9 letters with 7 generators > ▹ < a permutation group on 9 letters with 7 generators > ▹…▹1,2,3▹
The GroupTheory[CompositionSeries] and GroupTheory[CompositionLength] commands were introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
Download Help Document
What kind of issue would you like to report? (Optional)