FrattiniSubgroup - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/FrattiniSubgroup

GroupTheory

  

FrattiniSubgroup

  

construct the Frattini subgroup of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FrattiniSubgroup( G )

Parameters

G

-

a permutation group

Description

• 

The Frattini subgroup of a finite group G is the set of "non-generators" of G.  An element g of G is a non-generator if, whenever G is generated by a set S containing g, it is also generated by Sg.

• 

The Frattini subgroup of G is also equal to the intersection of the maximal subgroups of G. The Frattini subgroup of a finite group is nilpotent.

• 

The FrattiniSubgroup( G ) command returns the Frattini subgroup of a group G. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

GSmallGroup32,5:

FFrattiniSubgroupG

FΦ < a permutation group on 32 letters with 5 generators >

(1)

GroupOrderF

8

(2)

IsNilpotentF

true

(3)

FFrattiniSubgroupDihedralGroup12

FΦD12

(4)

GroupOrderF

2

(5)

GroupOrderFrattiniSubgroupAlt4

1

(6)

Compatibility

• 

The GroupTheory[FrattiniSubgroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[DihedralGroup]

GroupTheory[GroupOrder]

GroupTheory[IsNilpotent]

GroupTheory[SmallGroup]