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GroupTheory

  

Socle

  

construct the socle of a group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Socle( G )

Parameters

G

-

a permutation group

Description

• 

The socle of a group G is the subgroup generated by the minimal normal (non-trivial) subgroups of G.

• 

The Socle( G ) command constructs the socle of a group G. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

SSocleSymm4

S1,23,4,1,42,3

(1)

dfDirectFactorsS

df1,23,4,1,42,3

(2)

andmapIsSimple,df

true

(3)

SSocleAlt6

SA6

(4)

IsSubgroupAlt6,S

true

(5)

Compatibility

• 

The GroupTheory[Socle] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[DirectFactors]

GroupTheory[IsSimple]

GroupTheory[IsSubgroup]

GroupTheory[SymmetricGroup]