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Add efficiency note and infinite example to MaximalNormalSubgroups
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hungaborhorvath committed Nov 4, 2016
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Expand Up @@ -1761,9 +1761,19 @@ DeclareAttribute( "NilpotencyClassOfGroup", IsGroup );
## is a list containing those proper normal subgroups of the group <A>G</A>
## that are maximal among the proper normal subgroups. Returns fail if there
## are infinitely many maximal normal subgroups.
##
## Note, that the maximal normal subgroups of a group <A>G</A> can be
## computed more efficiently if the character table of <A>G</A> is known or
## if <A>G</A> is known to be abelian or solvable (even if infinite). So if
## the character table is needed, anyhow, or <A>G</A> is suspected to be
## abelian or solvable, then these should be computed before computing the
## maximal normal subgroups.
## <Example><![CDATA[
## gap> MaximalNormalSubgroups( g );
## [ Group([ (1,2,3), (2,3,4) ]) ]
## gap> f := FreeGroup("x", "y");; x := f.1;; y := f.2;;
## gap> List(MaximalNormalSubgroups(f/[x^2, y^2]), GeneratorsOfGroup);
## [ [ x, y*x*y^-1 ], [ y, x*y*x^-1 ], [ y*x^-1 ] ]
## gap> MaximalNormalSubgroups( AbelianGroup( [ 0 ] ) );
## fail
## ]]></Example>
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