construct the Fitting subgroup of a group
FittingSubgroup( G )
a permutation group
The Fitting subgroup of a finite group G is the unique largest normal nilpotent subgroup of G. Its existence and uniqueness is guaranteed by Fitting's Theorem, which asserts that the product of a family of normal and nilpotent subgroups of a finite group G is again a normal and nilpotent subgroup of G.
The Fitting subgroup of G is also equal to the (direct) product of the p-cores of G, as p ranges over the prime divisors of the order of G.
If G is a soluble group, then the Fitting subgroup of G is nontrivial.
The FittingSubgroup( G ) command constructs the Fitting subgroup of a group G. The group G must be an instance of a permutation group.
G ≔ Group⁡Perm⁡1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,Perm⁡1,2,5,3,4,7,6,9,8,11,10,13,16,15,12,14
F ≔ FittingSubgroup⁡G
F ≔ FittingSubgroup⁡Alt⁡4
The GroupTheory[FittingSubgroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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