GroupTheory
FrattiniSubgroup
construct the Frattini subgroup of a group
Calling Sequence
Parameters
Description
Examples
Compatibility
FrattiniSubgroup( G )
G
-
a group
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.
Since a quasicyclic group has no maximal subgroups, it is equal to its Frattini subgroup.
The GroupTheory[FrattiniSubgroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[AlternatingGroup]
GroupTheory[DihedralGroup]
GroupTheory[GroupOrder]
GroupTheory[IsNilpotent]
GroupTheory[QuasicyclicGroup]
GroupTheory[SmallGroup]
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