FrattiniSubgroup - Maple Help
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GroupTheory

  

FrattiniSubgroup

  

construct the Frattini subgroup of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FrattiniSubgroup( G )

Parameters

G

-

a group

Description

• 

The Frattini subgroup of a group  is the intersection of the maximal subgroups of , or  itself in case  has no maximal subgroups.

• 

The Frattini subgroup is equal to the set of "non-generators" of .  An element  of  is a non-generator if, whenever  is generated by a set  containing , it is also generated by .

• 

The Frattini subgroup of a finite group is nilpotent.

• 

The FrattiniSubgroup( G ) command returns the Frattini subgroup of a group G.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

Since a quasicyclic group has no maximal subgroups, it is equal to its Frattini subgroup.

(7)

(8)

(9)

(10)

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[QuasicyclicGroup]

GroupTheory[SmallGroup]

 


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