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Change StructureDescription for infinite cyclic group #3267

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Feb 6, 2019
Merged

Change StructureDescription for infinite cyclic group #3267

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9 changes: 5 additions & 4 deletions lib/grpnames.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -695,7 +695,8 @@ DeclareGlobalFunction( "LinearGroupParameters" );
## <Listing><![CDATA[
## StructureDescription(<G>) ::=
## 1 ; trivial group
## | C<size> ; cyclic group
## | C<size> ; finite cyclic group
## | Z ; infinite cyclic group
## | A<degree> ; alternating group
## | S<degree> ; symmetric group
## | D<size> ; dihedral group
Expand Down Expand Up @@ -759,7 +760,7 @@ DeclareGlobalFunction( "LinearGroupParameters" );
## If <A>G</A> is abelian, then decompose it into cyclic factors
## in <Q>elementary divisors style</Q>. For example,
## <C>"C2 x C3 x C3"</C> is <C>"C6 x C3"</C>.
## For infinite abelian groups, <C>"C0"</C> denotes the group of integers.
## For infinite abelian groups, <C>"Z"</C> denotes the group of integers.
## </Item>
## <Mark>3.</Mark>
## <Item>
Expand Down Expand Up @@ -883,9 +884,9 @@ DeclareGlobalFunction( "LinearGroupParameters" );
## gap> StructureDescription(SmallGroup(504,7):nice);
## "(C7 : Q8) : C9"
## gap> StructureDescription(AbelianGroup([0,2,3]));
## "C0 x C6"
## "Z x C6"
## gap> StructureDescription(AbelianGroup([0,0,0,2,3,6]):short);
## "0^3x6^2"
## "Z^3x6^2"
## gap> StructureDescription(PSL(4,2));
## "A8"
## ]]></Example>
Expand Down
32 changes: 21 additions & 11 deletions lib/grpnames.gi
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Expand Up @@ -490,7 +490,7 @@ local Ns,MinNs,sel,a,sz,j,gs,g,N;
Add(MinNs,Ns[a]);
for j in ShallowCopy(sel) do
if Size(Ns[j])>sz and Size(Ns[j]) mod sz=0 and IsSubset(Ns[j],Ns[a]) then
RemoveSet(sel,j);
RemoveSet(sel,j);
fi;
od;
od;
Expand Down Expand Up @@ -1672,23 +1672,35 @@ BindGlobal( "SD_insertsep", # function to join parts of name
return s;
end);

BindGlobal( "SD_cyclic",
function ( n )
if n = 0 or n = infinity then
return "Z";
fi;
return Concatenation("C",String(n));
end);

BindGlobal( "SD_cycsaspowers", # function to write C2 x C2 x C2 as 2^3, etc.
function ( name, cycsizes )

local short, d, k, j, n;
local short, g, d, k, j, n;

short := ValueOption("short") = true;
if not short then return name; fi;
RemoveCharacters(name," ");
cycsizes := Collected(cycsizes);
for n in cycsizes
do
for n in cycsizes do
d := n[1]; k := n[2];
g := SD_cyclic(d);
if d = 0 then
d := "Z";
else
d := String(d);
fi;
if k > 1 then
for j in Reversed([2..k]) do
name := ReplacedString(name,SD_insertsep(List([1..j],
i->Concatenation("C",String(d))),"x",""),
Concatenation(String(d),"^",String(j)));
name := ReplacedString(name,SD_insertsep(List([1..j],i->g),"x",""),
Concatenation(d,"^",String(j)));
od;
fi;
od;
Expand All @@ -1709,8 +1721,7 @@ BindGlobal( "StructureDescriptionForAbelianGroups", # for abelian groups
cycsizes := AbelianInvariants(G);
cycsizes := Reversed(ElementaryDivisorsMat(DiagonalMat(cycsizes)));
cycsizes := Filtered(cycsizes,n->n<>1);
return SD_cycsaspowers(SD_insertsep(List(cycsizes,
n->Concatenation("C",String(n))),
return SD_cycsaspowers(SD_insertsep(List(cycsizes, SD_cyclic),
" x ",""), cycsizes);
end );

Expand Down Expand Up @@ -1886,8 +1897,7 @@ BindGlobal( "StructureDescriptionForFiniteGroups", # for finite groups
if cyclics <> [] then
cycsizes := ElementaryDivisorsMat(DiagonalMat(List(cyclics,Size)));
cycsizes := Filtered(cycsizes,n->n<>1);
cycname := SD_cycsaspowers(SD_insertsep(List(cycsizes,
n->Concatenation("C",String(n))),
cycname := SD_cycsaspowers(SD_insertsep(List(cycsizes, SD_cyclic),
" x ",":."), cycsizes);
else cycname := ""; fi;
noncyclics := Difference(Gs,cyclics);
Expand Down
20 changes: 14 additions & 6 deletions tst/testinstall/opers/StructureDescription.tst
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Expand Up @@ -15,9 +15,9 @@ gap> StructureDescription(SmallGroup(504,7));
gap> StructureDescription(SmallGroup(504,7):nice);
"(C7 : Q8) : C9"
gap> StructureDescription(AbelianGroup([0,2,3]));
"C0 x C6"
"Z x C6"
gap> StructureDescription(AbelianGroup([0,0,0,2,3,6]):short);
"0^3x6^2"
"Z^3x6^2"
gap> StructureDescription(PSL(4,2));
"A8"

Expand All @@ -34,7 +34,7 @@ gap> List(AllPrimitiveGroups(DegreeAction, 8), StructureDescription);
[ "(C2 x C2 x C2) : C7", "(C2 x C2 x C2) : (C7 : C3)",
"(C2 x C2 x C2) : PSL(3,2)", "PSL(3,2)", "PSL(3,2) : C2", "A8", "S8" ]
gap> StructureDescription(AbelianGroup([0,0,0,2,3,6]):short);
"0^3x6^2"
"Z^3x6^2"
gap> G := Group([ (4,8)(6,10), (4,6,10,8,12), (2,4,12)(6,10,8), (3,9)(4,6,10,8,12)(7,11), (3,5)(4,6,10,8,12)(9,11), (1,3,11,9,5)(4,6,10,8,12) ]);;
gap> StructureDescription(G);
"A5 x A5"
Expand Down Expand Up @@ -87,9 +87,9 @@ true
gap> StructureDescriptionForFiniteSimpleGroups(Ree(27));
"Ree(27)"
gap> StructureDescription(AbelianGroup([0,0,0,2,3,4,5,6,7,8,9,10]));
"C0 x C0 x C0 x C2520 x C60 x C6 x C2 x C2"
"Z x Z x Z x C2520 x C60 x C6 x C2 x C2"
gap> StructureDescription(AbelianGroup([0,0,0,2,3,4,5,6,7,8,9,10]):short);
"0^3x2520x60x6x2^2"
"Z^3x2520x60x6x2^2"
gap> infolevel:=InfoLevel(InfoWarning);; SetInfoLevel(InfoWarning,2);
gap> StructureDescription(SmallGroup(48,16):recompute,nice);
#I Warning! Non-unique semidirect product:
Expand All @@ -104,7 +104,15 @@ gap> F := FreeGroup("r", "s");; r := F.1;; s := F.2;;
gap> G := F/[s^2, r^3, s*r*s*r];;
gap> StructureDescription(G);
"S3"

# some infinite groups
gap> G := F/[s*r*s^(-1)*r^(-1)];;
gap> StructureDescription(G);
"C0 x C0"
"Z x Z"
gap> StructureDescription(CyclicGroup(infinity));
"Z"
gap> StructureDescription(AbelianGroup([0,2,0]));
"Z x Z x C2"

#
gap> STOP_TEST("StructureDescription.tst", 1);