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Fix an error in the Modified Todd-Coxeter (subgroup presentations on specified generators) that could lead to wrong results when using IsomorphismFpGroupByGenerators #5469

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merged 1 commit into from
Jun 29, 2023
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Fix an error in the Modified Todd-Coxeter (subgroup presentations on specified generators) that could lead to wrong results when using IsomorphismFpGroupByGenerators #5469

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16 changes: 9 additions & 7 deletions lib/sgpres.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -3351,7 +3351,7 @@ local DATA,start,w,offset,c,i,j;
end );

DeclareGlobalName("NEWTC_ReplacedStringCyclic");
BindGlobal( "NEWTC_ReplacedStringCyclic", function(s,r)
BindGlobal( "NEWTC_ReplacedStringCyclic", function(s,r,cyc)
local p,new,start,half;
if Length(s)<Length(r) or Length(r)=0 then
return s;
Expand Down Expand Up @@ -3379,7 +3379,7 @@ local p,new,start,half;
new:=s;
fi;

if Length(r)=1 then
if Length(r)=1 or cyc=false then
return new; # no overlap or so possible
fi;

Expand All @@ -3399,7 +3399,8 @@ local p,new,start,half;
# second half arises later. Does also first half arise -- if so we need
# to go through once more
if new{[p-half+1..p-1]}=r{[1..half-1]} then
return NEWTC_ReplacedStringCyclic(new,r);
new:=NEWTC_ReplacedStringCyclic(new,r,cyc);
return new;
fi;
fi;

Expand Down Expand Up @@ -3540,8 +3541,8 @@ local DATA,rels,i,j,w,f,r,s,fam,ri,a,offset,rset,re,stack,pres,
ri:=Length(r);
# reduce with others
for j in rels do
r:=NEWTC_ReplacedStringCyclic(r,j);
r:=NEWTC_ReplacedStringCyclic(r,-Reversed(j));
r:=NEWTC_ReplacedStringCyclic(r,j,true);
r:=NEWTC_ReplacedStringCyclic(r,-Reversed(j),true);
od;
Info(InfoFpGroup,3,"Relatorlen ",ri,"->",Length(r));

Expand All @@ -3557,7 +3558,7 @@ local DATA,rels,i,j,w,f,r,s,fam,ri,a,offset,rset,re,stack,pres,
while j<=Length(rels) do
s:=rels[j];
for re in rset do;
s:=NEWTC_ReplacedStringCyclic(s,re);
s:=NEWTC_ReplacedStringCyclic(s,re,true);
od;
if not IsIdenticalObj(s,rels[j]) then
if Length(s)>0 then
Expand All @@ -3578,7 +3579,8 @@ local DATA,rels,i,j,w,f,r,s,fam,ri,a,offset,rset,re,stack,pres,
s:=DATA.aug[a+offset][j];
if Length(s)>=Length(r) then
for re in rset do
s:=NEWTC_ReplacedStringCyclic(s,re);
# NOT cyclic replace!
s:=NEWTC_ReplacedStringCyclic(s,re,false);
od;
DATA.aug[a+offset][j]:=s;
fi;
Expand Down
11 changes: 11 additions & 0 deletions tst/testbugfix/2023-06-28-MTC.txt
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Original file line number Diff line number Diff line change
@@ -0,0 +1,11 @@
# Overly eager cyclic replace in MTC, #5467

gap> f := FreeGroup(4);;
gap> g := f / [f.1^2, f.2^2, f.3^2, f.4^2, (f.1*f.4)^2, (f.2*f.4)^2,
> (f.3*f.4)^4, (f.1*f.2)^4, (f.1*f.3)^2, (f.2*f.3)^4, (f.1*f.2*f.3*f.2)^3,
> (f.2*f.3*f.4*f.3)^3];;
gap> h := Subgroup(g, [g.1,g.2,g.3]);;
gap> iso2 := IsomorphismFpGroupByGenerators(h, GeneratorsOfGroup(h));;
gap> h2 := Image(iso2);;
gap> Size(h2);
72