# GAP:IsContranormal

From Groupprops

## Definition

### 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.

### Behavior

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);

## Method

### Code

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