compute the k-th transitive of a given degree
compute the number of transitive groups of a given degree
compute all the transitive groups of a given degree
TransitiveGroup( d, k )
NumTransitiveGroups( d )
AllTransitiveGroups( d )
: posint : the degree
: posint : an index
These three commands form an interface to the transitive groups database in the GroupTheory package. Currently, conjugacy class representatives of the transitive groups up to degree 37, but excluding those of degree 32, are available in the database.
The NumTransitiveGroups( d ) command returns the number of transitive groups of degree d stored in the transitive groups database. If the value returned is 0, this indicates that no transitive groups of degree d are in the database. (It does not indicate that there are no transitive groups of that degree!)
The TransitiveGroup( d, k ) command returns the k-th transitive group of degree d from the transitive groups database. If k is larger than the number of transitive groups of degree d, an exception is raised.
The AllTransitiveGroups( d ) command returns a list of all the transitive groups of degree d. It is essentially equivalent to [seq]( TransitiveGroup( d, k ), k = 1 .. NumTransitiveGroups( d ) ), but avoids some repeated checks.
Transitive groups of prime degree are primitive.
For groups of non-prime degree, we normally find imprimitive groups.
The GroupTheory[TransitiveGroup], GroupTheory[NumTransitiveGroups] and GroupTheory[AllTransitiveGroups] commands were introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
Download Help Document
What kind of issue would you like to report? (Optional)