GAP:IsPolynormal

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 two groups are subgroups of a common big group, and the second group is a contranormal subgroup in its closure under the action by conjugation by the cyclic subgroup generated by any element of the first group.
• The function returns false if the two groups are subgroups of a common big group, and the above condition is violated.
• If the two groups are not subgroups of a common big group, or if the arguments provided are not groups, the function returns a NoMethodFound error.

Related functions

• GAP:IsPronormal
• GAP:IsParanormal

Method

Code

IsPolynormal := function(G,H)
	local K,g;
	for g in Set(G) do
	    K := NormalClosure(Group(g),H);
	    if (not NormalClosure(K,H) = K) then return false; fi;
	od;
	return true;
end;;