Complement( U, N )
Let N and U be ag group such that N is a normal subgroup of U.
Complement
returns a complement of N in U if the U splits over
N. Otherwise false
is returned.
Complement
descends along an elementary abelian series of U
containing N. See CNW90 for details.
gap> v4 := Subgroup( s4, [ c, d ] ); Subgroup( s4, [ c, d ] ) gap> Complement( s4, v4 ); Subgroup( s4, [ a, b ] ) gap> z4 := CyclicGroup( AgWords, 4 ); Group( c4_1, c4_2 ) gap> z2 := Subgroup( z4, [ z4.2 ] ); Subgroup( Group( c4_1, c4_2 ), [ c4_2 ] ) gap> Complement( z4, z2 ); false gap> m9 := ElementaryAbelianGroup( AgWords, 9 ); Group( m9_1, m9_2 ) gap> m3 := Subgroup( m9, [ m9.2 ] ); Subgroup( Group( m9_1, m9_2 ), [ m9_2 ] ) gap> Complement( m9, m3 ); Subgroup( Group( m9_1, m9_2 ), [ m9_1 ] )
GAP 3.4.4