GroupTheory
FrattiniSeries
construct the Frattini series of a group
FrattiniLength
return the Frattini length of a group
Calling Sequence
Parameters
Description
Examples
Compatibility
FrattiniSeries( G )
FrattiniLength( G )
G
-
a permutation group
The Frattini series of a group is the descending normal series of whose terms are the successive Frattini subgroups, defined as follows. Let and, for , define . The sequence
of distinct terms is called the Frattini series of . The number is called the Frattini length of .
The FrattiniSeries( G ) command constructs the Frattini series of a group G. The group G must be an instance of a permutation group. The Frattini series of G is represented by a series data structure which admits certain operations common to all series. See GroupTheory[Series].
Since the group G is required to be finite, the Frattini series always terminates in the trivial subgroup.
The FrattiniLength( G ) command returns the Frattini length of G; that is, the length of the Frattini series of G. This is the number of subgroup inclusions - so it is one less than the number of groups in the Frattini series.
The GroupTheory[FrattiniSeries] and GroupTheory[FrattiniLength] commands were introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
See Also
GroupTheory[DihedralGroup]
GroupTheory[FrattiniSubgroup]
GroupTheory[FrobeniusGroup]
GroupTheory[LowerPCentralSeries]
GroupTheory[Series]
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