Break loop using ConjugacyClasses on Centralizer in permutation group

[jackschmidt]

GAP has trouble computing conjugacy classes in certain subgroups of a permutation group. I observed the problem in the ubuntu gap (4.8.8) and tried the latest release, but got the same result.

The reproducer code is:

wreathy := WreathProduct(SymmetricGroup(2),SymmetricGroup(5));;
classes := ConjugacyClasses(wreathy);;
badsubgroup := StabilizerOfExternalSet( classes[2] );;
ConjugacyClasses( badsubgroup );

One can use:

ConjugacyClasses( Group( GeneratorsOfGroup( badsubgroup ) ) );

to get the conjugacy classes, so it is something wrong with stored attributes. The trouble does not show up if the original group is solvable. The bad subgroup is solvable.

 *********   GAP 4.10.0 of 01-Nov-2018
 *  GAP  *   https://www.gap-system.org
 *********   Architecture: x86_64-pc-linux-gnu-default64
 Configuration:  gmp 6.1.2, readline
 Loading the library and packages ...
 Packages:   AClib 1.3.1, Alnuth 3.1.0, AtlasRep 1.5.1, AutoDoc 2018.09.20, AutPGrp 1.10, Browse 1.8.8, Carat 2.2.2, 
             CRISP 1.4.4, Cryst 4.1.18, CrystCat 1.1.8, CTblLib 1.2.2, FactInt 1.6.2, FGA 1.4.0, GAPDoc 1.6.2, IO 4.5.4, 
             IRREDSOL 1.4, LAGUNA 3.9.0, Polenta 1.3.8, Polycyclic 2.14, PrimGrp 3.3.2, RadiRoot 2.8, ResClasses 4.7.1, 
             SmallGrp 1.3, Sophus 1.24, SpinSym 1.5, TomLib 1.2.7, TransGrp 2.0.4, utils 0.59
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> wreathy := WreathProduct(SymmetricGroup(2),SymmetricGroup(5));;
gap> classes := ConjugacyClasses(wreathy);;
gap> badsubgroup := StabilizerOfExternalSet( classes[2] );;
gap> ConjugacyClasses( badsubgroup );
Error, List Element: <list>[5] must have an assigned value in
  img{[ i .. r ]} := OnTuples( img{[ i .. r ]}, H.transversal[img[i]] ); at /home/jack/gap-4.10.0/lib/pcgsperm.gi:806 called from 
ExponentsOfPcElementPermGroup( pcgs, g, 1, Maximum( poss ), 'e' ) at /home/jack/gap-4.10.0/lib/pcgsperm.gi:1261 called from
ExponentsOfPcElement( ParentPcgs( pcgs ), elm, pcgs!.depthsInParent{range} ) at /home/jack/gap-4.10.0/lib/pcgsind.gi:1486 called from
ExponentsOfPcElement( ParentPcgs( pcgs ), elm, pcgs!.depthsInParent{range} ) at /home/jack/gap-4.10.0/lib/pcgsind.gi:1486 called from
ExponentsOfPcElement( NumeratorOfModuloPcgs( pcgs ), elm, pcgs!.depthMap ) at /home/jack/gap-4.10.0/lib/pcgsmodu.gi:931 called from
ExponentsOfPcElement( Npcgs, Comm( h, c ) ) at /home/jack/gap-4.10.0/lib/clashom.gi:1735 called from
...  at *stdin*:4
you can 'return;' after assigning a value
brk> Where(300);
ExponentsOfPcElementPermGroup( pcgs, g, 1, Maximum( poss ), 'e' ) at /home/jack/gap-4.10.0/lib/pcgsperm.gi:1261 called from
ExponentsOfPcElement( ParentPcgs( pcgs ), elm, pcgs!.depthsInParent{range} ) at /home/jack/gap-4.10.0/lib/pcgsind.gi:1486 called from
ExponentsOfPcElement( ParentPcgs( pcgs ), elm, pcgs!.depthsInParent{range} ) at /home/jack/gap-4.10.0/lib/pcgsind.gi:1486 called from
ExponentsOfPcElement( NumeratorOfModuloPcgs( pcgs ), elm, pcgs!.depthMap ) at /home/jack/gap-4.10.0/lib/pcgsmodu.gi:931 called from
ExponentsOfPcElement( Npcgs, Comm( h, c ) ) at /home/jack/gap-4.10.0/lib/clashom.gi:1735 called from
LiftClassesEANonsolvGeneral( G, mpcgs, i, hom, pcisom, solvtriv, fran ) at /home/jack/gap-4.10.0/lib/clashom.gi:2469 called from
ConjugacyClassesViaRadical( G ) at /home/jack/gap-4.10.0/lib/clashom.gi:3071 called from
<function "unknown">( <arguments> )
 called from read-eval loop at *errin*:1
brk> StructureDescription( badsubgroup );
"C2 x (((((C2 x C2 x C2 x C2) : C2) : C2) : C3) : C2)"
brk> 
gap> ConjugacyClasses( Group( GeneratorsOfGroup( badsubgroup ) ) );
[ ()^G, (3,4)(7,8)^G, (1,2)(3,4)(5,6)(7,8)^G, (1,7)(2,8)(3,5)(4,6)^G, (1,8,2,7)(3,5,4,6)^G, (1,7,5)(2,8,6)^G, 
  (1,8,6,2,7,5)(3,4)^G, (5,7)(6,8)^G, (3,4)(5,8,6,7)^G, (1,2)(3,4)(5,7)(6,8)^G, (1,7,3,5)(2,8,4,6)^G, (7,8)^G, 
  (1,2)(3,4)(7,8)^G, (1,7,2,8)(3,5)(4,6)^G, (1,7,6,2,8,5)^G, (1,8,5)(2,7,6)(3,4)^G, (5,7,6,8)^G, (3,4)(5,8)(6,7)^G, 
  (1,2)(3,4)(5,7,6,8)^G, (1,7,4,6,2,8,3,5)^G, (9,10)^G, (3,4)(7,8)(9,10)^G, (1,2)(3,4)(5,6)(7,8)(9,10)^G, 
  (1,7)(2,8)(3,5)(4,6)(9,10)^G, (1,8,2,7)(3,5,4,6)(9,10)^G, (1,7,5)(2,8,6)(9,10)^G, (1,8,6,2,7,5)(3,4)(9,10)^G, 
  (5,7)(6,8)(9,10)^G, (3,4)(5,8,6,7)(9,10)^G, (1,2)(3,4)(5,7)(6,8)(9,10)^G, (1,7,3,5)(2,8,4,6)(9,10)^G, (7,8)(9,10)^G, 
  (1,2)(3,4)(7,8)(9,10)^G, (1,7,2,8)(3,5)(4,6)(9,10)^G, (1,7,6,2,8,5)(9,10)^G, (1,8,5)(2,7,6)(3,4)(9,10)^G, 
  (5,7,6,8)(9,10)^G, (3,4)(5,8)(6,7)(9,10)^G, (1,2)(3,4)(5,7,6,8)(9,10)^G, (1,7,4,6,2,8,3,5)(9,10)^G ]

[markuspf]

Note that this does not happen with the current master branch (but it does happen on stable-4.10

[markuspf]

Cherry picking commit 75f11d9 makes the problem go away.

[markuspf]

This is probably one for @hulpke. While I could determine that ExponentsOfPcElement is passed an element that does not belong to the group, I have no idea why this happens. The following still happens on the master branch:

gap> wreathy := WreathProduct(SymmetricGroup(2),SymmetricGroup(5));;
gap> classes := ConjugacyClasses(wreathy);;
gap> badsubgroup := StabilizerOfExternalSet( classes[2] );;
gap> ConjugacyClassesViaRadical(badsubgroup);
Error, List Element: <list>[5] must have an assigned value in
  img{[ i .. r ]} := OnTuples( img{[ i .. r ]}, H.transversal[img[i]] ); at /home/mp397/git/gap/lib/pcgsperm.gi:807 called from 
ExponentsOfPcElementPermGroup( pcgs, g, 1, Maximum( poss ), 'e' ) at /home/mp397/git/gap/lib/pcgsperm.gi:1262 called from
ExponentsOfPcElement( ParentPcgs( pcgs ), elm, pcgs!.depthsInParent{range} ) at /home/mp397/git/gap/lib/pcgsind.gi:1487 called from
ExponentsOfPcElement( ParentPcgs( pcgs ), elm, pcgs!.depthsInParent{range} ) at /home/mp397/git/gap/lib/pcgsind.gi:1487 called from
ExponentsOfPcElement( NumeratorOfModuloPcgs( pcgs ), elm, pcgs!.depthMap ) at /home/mp397/git/gap/lib/pcgsmodu.gi:932 called from
ExponentsOfPcElement( Npcgs, Comm( h, c ) ) at /home/mp397/git/gap/lib/clashom.gi:1742 called from
...  at *stdin*:7
type 'quit;' to quit to outer loop

[jackschmidt]

Thanks! I worry that ConjugacyClassesFittingFreeGroup is running on a non-trivial solvable group (on master branch).

gap> SetAssertionLevel(99);
gap> ConjugacyClassesViaRadical(badsubgroup);
Error, Assertion failure in
  Sum( List( cl, function ( pair )
          return Size( G ) / Size( pair[2] );
      end ) ) = Size( G ) at /home/jack/gap/lib/clashom.gi:1495 called from 
ConjugacyClassesFittingFreeGroup( f ) at /home/jack/gap/lib/clashom.gi:2402 called from
<function "ConjugacyClassesViaRadical">( <arguments> )
 called from read-eval loop at *stdin*:5
you may 'return;'
brk> f;
Group([ (1,3)(2,4), (1,7,5,3)(2,8,6,4), (), (), (), (), () ])
brk> StructureDescription(f);
"S4"

[hulpke]

@markuspf 75f11d9 is a red herring, just works around problem.