GroupTheory
IsCharacteristicallySimple
determine whether a group is characteristically simple
Calling Sequence
Parameters
Description
Examples
IsCharacteristicallySimple( G )
G
-
a group
A group G is characteristically simple if it is non-trivial and has no proper, non-trivial characteristic subgroups. Clearly, every simple group is characteristically simple.
The IsCharacteristicallySimple( G ) command returns true if the group G is characteristically simple, and returns false otherwise.
withGroupTheory:
IsCharacteristicallySimpleCyclicGroup37
true
IsCharacteristicallySimpleCyclicGroup300
false
IsCharacteristicallySimpleAlt8
IsCharacteristicallySimpleSymm8
IsCharacteristicallySimpleSmallGroup8,5
IsCharacteristicallySimpleSmallGroup8,2
IsCharacteristicallySimpleDirectProductAlt5,Alt6
IsCharacteristicallySimpleDirectProductAlt6,Alt6
See Also
GroupTheory[IsSimple]
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