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Function type

IsContranormal is a GAP function defined here that takes as input two groups and outputs a Boolean value. It is not a built-in GAP command.


The behavior is as follows:

  • The function returns true if the second group is a contranormal subgroup of the first group.
  • The function returns false if the second group is a subgroup that is not contranormal in the first group, or alternatively, if the second group is not contained inside the first group, but they are contained inside a common big group.
  • If one of the arguments provided is not a group, or if the two groups are not subgroups of a common big group, GAP returns a NoMethodFound error.

Typical use

The typical use is in the form:

IsContranormal(group, subgroup);



IsContranormal := function(G,H)
       return(NormalClosure(G,H) = G);