2017-10-16 19:43:09 +00:00
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#############################################################################
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##
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#W iso.tst Testing isomorphisms G. P. Nagy / P. Vojtechovsky
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##
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2017-10-30 03:54:13 +00:00
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#H @(#)$Id: iso.tst, v 3.4.0 2017/10/26 gap Exp $
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2017-10-16 19:43:09 +00:00
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##
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#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary),
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#Y P. Vojtechovsky (University of Denver, USA)
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##
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gap> START_TEST("LOOPS, iso: testing isomorphisms");
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# TESTING DISCIMINATOR
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gap> Length( Discriminator( MoufangLoop( 12, 1 ) )[ 1 ] );
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3
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# TESTING AUTOMORPHISM GROUPS
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gap> AutomorphismGroup( MoufangLoop( 12, 1 ) );
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<permutation group with 14 generators>
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gap> AutomorphismGroup( MoufangLoop( 64, 1235 ) );
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<permutation group with 16 generators>
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gap> Size( last );
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512
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gap> AutomorphismGroup( LeftBolLoop( 8, 1 ) );
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Group([ (5,8)(6,7), (2,3)(6,7), (2,6)(3,7), (2,7)(3,6) ])
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gap> Size( AutomorphismGroup( SteinerLoop( 16, 77 ) ) );
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3
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gap> Q := QuasigroupByCayleyTable([[3,2,1],[2,1,3],[1,3,2]]);;
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gap> AutomorphismGroup( Q );
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Group([ (1,2,3), (1,3,2) ])
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# TESTING ISOMORPHISMS
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gap> Q := DirectProduct( MoufangLoop( 32, 5 ) );;
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gap> Qp := IsomorphicCopyByPerm( Q, (2,3,4)(17,20) );;
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2017-10-30 03:54:13 +00:00
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gap> Qq := LoopIsomorph( Q, (2,3,4)(17,20) );;
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gap> Qp = Qq;
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false
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gap> CayleyTable( Qp ) = CayleyTable( Qq );
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true
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2017-10-16 19:43:09 +00:00
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gap> IsomorphismLoops( Q, Qp );
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(2,3,4)(18,23)(19,25)(21,27)(22,28)(24,30)(26,31)(29,32)
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gap> LoopsUpToIsomorphism( [Q,Qp] );
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[ <Moufang loop 32/5> ]
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gap> Q2 := QuasigroupByCayleyTable( [[2,1],[1,2]] );;
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gap> IsomorphismQuasigroups( Q2, IntoLoop(CyclicGroup(2)) );
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(1,2)
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gap> Length( QuasigroupsUpToIsomorphism( [Q,Q2] ) );
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2
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# TESTING ISOTOPISMS
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gap> IsotopismLoops( SmallLoop( 5, 1 ), SmallLoop( 5, 4 ) );
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[ (3,4,5), (1,2), (1,2) ]
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gap> STOP_TEST( "iso.tst", 10000000 );
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