GroupTheory
IsQuasisimple
determine whether a group is quasi-simple
Calling Sequence
Parameters
Description
Examples
IsQuasisimple( G )
G
-
a permutation group
A group G is quasi-simple if it is perfect and its central quotient is simple. In particular, every simple non-abelian group is quasi-simple.
The IsQuasisimple( G ) command returns true if the group G is quasi-simple, and returns false otherwise.
withGroupTheory:
The trivial group is perfect, but its central quotient is itself trivial, hence, not simple.
IsQuasisimpleTrivialGroup
false
IsQuasisimpleSymm4
IsQuasisimpleGL2,4
IsQuasisimpleSL2,5
true
IsQuasisimpleSL2,7
IsQuasisimplePerfectGroup1920,3
IsQuasisimplePSO−1,4,5
See Also
GroupTheory[IsSimple]
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