GAP:IsParanormal

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Definition

Function type

The function takes as input two groups and outputs a Boolean variable.

Behavior

The function behaves as follows:

  • If the two group are subgroups of a common big group, and the second subgroup is a contranormal subgroup in the subgroup generated by it and any conjugate of it by an element of the first group, the function returns true.
  • If the two groups are subgroups of a common big group, and the above condition is violated ,the function returns false
  • If the two arguments provided are not groups, or if they are not subgroups of a common big group, GAP returns a NoMethodFound error.

Method

Code

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