construct the Frattini subgroup of a group
FrattiniSubgroup( G )
a permutation group
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 S∖g.
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.
F≔Φ⁡ < a permutation group on 32 letters with 5 generators >
The GroupTheory[FrattiniSubgroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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