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.
The typical use is in the form:
IsContranormal := function(G,H) return(NormalClosure(G,H) = G); end;;