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GroupTheory

  

TransitiveGroup

  

compute the k-th transitive of a given degree

  

NumTransitiveGroups

  

compute the number of transitive groups of a given degree

  

AllTransitiveGroups

  

compute all the transitive groups of a given degree

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

TransitiveGroup( d, k )

NumTransitiveGroups( d )

AllTransitiveGroups( d )

Parameters

d

-

: posint : the degree

k

-

: posint : an index

Description

• 

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.

Examples

withGroupTheory:

NumTransitiveGroups31

12

(1)

GTransitiveGroup31,3

G2,12,223,13,234,14,245,15,256,16,267,17,278,18,289,19,2910,20,3011,21,31,1,2,26,3,20,22,27,30,14,4,16,25,21,13,24,23,8,9,28,6,10,31,19,29,15,12,7,5,18,11,17

(2)

IsTransitiveG

true

(3)

IsPrimitiveG

true

(4)

LAllTransitiveGroups31:nopsL

12

(5)

andmapIsTransitive,L

true

(6)

Transitive groups of prime degree are primitive.

andmapIsPrimitive,L

true

(7)

For groups of non-prime degree, we normally find imprimitive groups.

NumTransitiveGroups8

50

(8)

nopsremoveIsPrimitive,AllTransitiveGroups8

43

(9)

Compatibility

• 

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.

See Also

GroupTheory

GroupTheory[IsPrimitive]

GroupTheory[IsTransitive]

Perm