GAP:IsSelfCentralizing

Definition

Function type

The function takes in two arguments, both of them groups, and outputs a Boolean variable.

Behavior

• The function returns true if both groups are subgroups of a common big group, and if the centralizer of the second group in the first is also contained in the second subgroup.
• The function returns false if the two groups are subgroups of a common big group, and if the centralizer of the second group in the first is not contained in the second group.
• If the two groups are not contained in a common big group, the function returns a NoMethodFound error.

Typical usage

The function is typically invoked as follows:

IsSelfCentralizing(group,subgroup);

The function returns true if the subgroup is a self-centralizing subgroup of the whole group and false otherwise.

Related functions

• GAP:IsSelfNormalizing

Method

Code

IsSelfCentralizing := function(G,H)
	return (Centralizer(G,H) <= H);
end;;