GAP:IsFullinvariant

Package requirement
This function is part of the SONATA package.

Function type
The function takes as input two arguments, both of which are groups, and outputs a boolean answer (true/false).

Behavior

 * The function returns true if the second group is a subgroup of the first, and is fully characteristic in it.
 * The function returns false if the second group is a subgroup of the first, but is not fully characteristic.
 * If the second group is not a subgroup of the first group, but they are both subgroups of a common big group, the function returns a usage error.
 * If the two arguments are not groups, or if they are not contained in a common parent group, the function returns a NoMethodFound error.

Examples of usage
gap> G := SmallGroup(81,7);  gap> H := Center(G); Group([ f4 ]) gap> IsFullinvariant(G,H); true gap> IsFullinvariant(H,G); Error, usage: Images, Images, Images called from Images( m, U ) called from func( elm ) called from ForAll( maps, function ( m )     return IsSubset( U, Images( m, U ) );  end ) called from IsInvariantUnderMaps( G, U, Endomorphisms( G ) ) called from called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> IsFullinvariant(CyclicGroup(3),SymmetricGroup(3)); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `IsFullinvariant' on 2 arguments called from Error( "usage: Images, Images, Images" ); called from Images( m, U ) called from func( elm ) called from ForAll( maps, function ( m )     return IsSubset( U, Images( m, U ) );  end ) called from IsInvariantUnderMaps( G, U, Endomorphisms( G ) ) called from ... Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue