# GAP:IsSelfNormalizing

From Groupprops

## Definition

### Function type

The function takes as input two arguments, both of which are groups, and outputs a boolean variable.

### Behavior

The function behaves as follows:

- If the two groups are contained in a common big group and the normalizer of the second group in the first group is
*also*contained in the second group, the function returns`true`. In other words, if the groups are and , the function returns`true`. - If the two groups are in a common big group, but the normalizer of the second group in the first group is
*not*contained in the second group, the function returns`false`. - If the two subgroups are not subgroups of a common big group, GAP returns a
`NoMethodFound`error.

### Typical usage

The typical usage is as follows:

IsSelfNormalizing(group,subgroup);

This returns `true` if and only if the subgroup is a self-normalizing subgroup of the whole group.

## Method

### Code

IsSelfCentralizing := function(G,H) return IsSubgroup(H, Normalizer(G,H)); end;;