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REBASE: Subsequenct examples
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hulpke committed Sep 17, 2020
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8 changes: 4 additions & 4 deletions doc/tut/group.xml
Original file line number Diff line number Diff line change
Expand Up @@ -866,17 +866,17 @@ lie in one orbit under the group,
<Example><![CDATA[
gap> rep := RepresentativeAction( a8, (1,2)(3,4)(5,6)(7,8),
> (1,3)(2,4)(5,7)(6,8) );
(1,5,6,8,4,3)(2,7)
(2,3)(6,7)
gap> u15 := ClosureGroup( u105, rep );; Index( a8, u15 );
15
]]></Example>
<P/>
<C>u15</C> is of course a maximal subgroup, because <C>a8</C> has no subgroups of
index 3 or&nbsp;5. There is in fact another class of subgroups of index 15
above <C>u105</C> that we get by adding <C>(2,3)(6,7)</C> to <C>u105</C>.
above <C>u105</C> that we get by adding <C>(2,3)(6,8)</C> to <C>u105</C>.
<P/>
<Example><![CDATA[
gap> u15b := ClosureGroup( u105, (2,3)(6,7) );; Index( a8, u15b );
gap> u15b := ClosureGroup( u105, (2,3)(6,8) );; Index( a8, u15b );
15
gap> RepresentativeAction( a8, u15, u15b );
fail
Expand Down Expand Up @@ -1181,7 +1181,7 @@ gap> niceaut := NiceObject( aut );
Group([ (1,4,2,3), (1,5,4)(2,6,3), (1,2)(3,4), (3,4)(5,6) ])
gap> IsomorphismGroups( niceaut, SymmetricGroup( 4 ) );
[ (1,4,2,3), (1,5,4)(2,6,3), (1,2)(3,4), (3,4)(5,6) ] ->
[ (1,4,3,2), (1,3,2), (1,3)(2,4), (1,2)(3,4) ]
[ (1,4,2,3), (2,3,4), (1,2)(3,4), (1,4)(2,3) ]
]]></Example>
<P/>
The range of a nice monomorphism is in most cases a permutation group,
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