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############################################################################
##
#W permut.tst GAP tests ABB&ECL&RER
##
##
#Y Copyright (C) 2015-2018, Adolfo Ballester-Bolinches, Enric Cosme-Ll\'opez,
## and Ramon Esteban-Romero
##
## This file tests some functions that deal with permutability
##
gap> START_TEST("permut.tst");
gap> sym4:=SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> ArePermutableSubgroups(sym4, Subgroup(sym4, [(1,2)(3,4)]), Subgroup(sym4, [(1,2,3)]));
false
gap> List(Set(AllSubnormalSubgroups(sym4), IdGroup));
[ [ 1, 1 ], [ 2, 1 ], [ 4, 2 ], [ 12, 3 ], [ 24, 12 ] ]
gap> IsTGroup(SymmetricGroup(3));
true
gap> IsPTGroup(ExtraspecialGroup(125, 5));
false
gap> IsPTGroup(ExtraspecialGroup(125, 25));
true
gap> IdsOfAllSmallGroups(Size, 48, IsPTGroup, true) =
> [ [ 48, 1 ], [ 48, 2 ], [ 48, 4 ], [ 48, 5 ], [ 48, 9 ], [ 48, 10 ],
> [ 48, 11 ], [ 48, 20 ], [ 48, 23 ], [ 48, 24 ], [ 48, 34 ], [ 48, 35 ],
> [ 48, 40 ], [ 48, 42 ], [ 48, 44 ], [ 48, 46 ], [ 48, 51 ], [ 48, 52 ] ];
true
gap> IsSCGroup(Group((3,7,5)(4,8,6), (1,2,6)(3,4,8), (9,10,11,12,13)));
true
gap> ArePermutableSubgroups(sym4, AlternatingGroup(4), Subgroup(sym4, [(1,2,3,4), (1,3)]));
true
gap> OnePairShowingNotTotallyPermutableSubgroups(sym4, AlternatingGroup(4), Subgroup(sym4, [(1,2,3,4), (1,3)]));
[ Group([ (2,4,3) ]), Group([ (1,2)(3,4) ]) ]
gap> Size(Permutizer(sym4, Subgroup(sym4, [(1,2,3)])));
6
gap> "The following result was wrong in previous versions of permut\n";
"The following result was wrong in previous versions of permut\n"
gap> g:=SymmetricGroup(3);;h:=Subgroup(g,[(1,2,3)]);;k:=Subgroup(h,[(1,2,3)]);;
gap> OneSubgroupInWhichSubnormalNotPermutable(g,k);
fail
gap> STOP_TEST( "permut.tst", 7000000 );
##############################################################################
##
#E
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