GAP:IsIsomorphConjugateSubgroup

Definition

Function type

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

Behavior

• The function returns true if the second group is a subgroup of the first, and is an isomorph-conjugate subgroup: it is conjugate to every subgroup of the first group isomorphic to it.
• The function returns false if both groups are contained in a common big group, and the second group is not a subgroup of the first, or if the second group is a subgroup of the first but is not isomorph-conjugate in the first group.

Typical usage

The typical usage of the function is as:

IsIsomorphConjugateSubgroup(group,subgroup);

Method

Code

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