GAP:IsIsomorphFreeSubgroup

Definition

Function type

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

Behavior

• The function returns true if the second group is a subgroup of the first, and is an isomorph-free subgroup: there is no other subgroup of the first group isomorphic to the second subgroup.
• The function returns false if both groups live in the same big group but the second group is not a subgroup of the first, or if the second group is a subgroup but is not isomorph-free in the first.

Typical usage

The typical invocation is as follows:

IsIsomorphFreeSubgroup(group,subgroup);

Related functions

• GAP:IsCharacteristicSubgroup
• GAP:IsAutomorphConjugateSubgroup
• GAP:IsIsomorphConjugateSubgroup

Method

Code

IsIsomorphFreeSubgroup := function(G,H)
	return(IsSubgroup(G,H) and IsNormal(G,H) and Length(IsomorphicSubgroups(G,H)) = 1);
end;;