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^ Subject:

gap forum gap-forum.

Hallo,

if you want a short overwiew of the Subgroups - f.i. s4 -

then use the little program

L:=[];

Net:=function(lat,m)

# shows an overview of the lattice

# lat: name of LatticeSubgroups, a: number of the ConjugacyClasses

local i;

for i in [1..m] do

L:=List(ConjugacyClassesSubgroups(lat)[i],Size);Print(L,"

",Length(L),"\n");

od;

end;

gap> s4:=SymmetricGroup(4); Sym( [ 1 .. 4 ] ) gap> lat:=LatticeSubgroups(s4); <subgroup lattice of Sym( [ 1 .. 4 ] ), 11 classes, 30 subgroups> gap> Net(lat,11); [ 1 ] 1 [ 2, 2, 2 ] 3 [ 2, 2, 2, 2, 2, 2 ] 6 [ 3, 3, 3, 3 ] 4 [ 4 ] 1 [ 4, 4, 4 ] 3 [ 4, 4, 4 ] 3 [ 6, 6, 6, 6 ] 4 [ 8, 8, 8 ] 3 [ 12 ] 1 [ 24 ] 1

If you want to see a distinct Subgroup use the following

NetSubgroup:=function(lat,a,b)

# shows a distinct Subgroup

# lat: name of LatticeSubgroups, a: number of the wanted ConjugacyClass,

# b: number of the wanted Subgroup

return ConjugacyClassesSubgroups(lat)[a][b];

end;

gap> NetSubgroup(lat,9,2); Group([ (2,4), (1,3), (1,4)(2,3) ])

if you want to see all the groups of ConjugacyClass then use

NetSubgroups:=function(lat,a,n1,n2)

# lat: name of LatticeSubgroups, a: number of the wanted ConjugacyClass

# n1: first Subgroup, n2: last Subgroup of the ConjugacyClass

local i;

for i in [n1..n2] do Print (ConjugacyClassesSubgroups(lat)[a][i], "\n");od;

end;

gap> NetSubgroups(lat,9,1,3); Group( [ (3,4), (1,2), (1,3)(2,4) ] ) Group( [ (2,4), (1,3), (1,4)(2,3) ] ) Group( [ (2,3), (1,4), (1,2)(3,4) ] )

Best wishes

K.Ewald

-----Ursprüngliche Nachricht-----

Von: GAP-Forum-Sender@dcs.st-and.ac.uk

[mailto:GAP-Forum-Sender@dcs.st-and.ac.uk]Im Auftrag von Bjorn

Vandenbergh

Gesendet: Donnerstag, 23. November 2000 16:36

An: Multiple recipients of list

Betreff: Subgroup Lattice??

Hello,

I'm a last years student in mathematics and I'm making my thesis. The

name will probably be "Working algebraic with groups: an acquintance

with Gap". In this matter I'm studying the Lattice of subgroups of a

permutation group with Gap. I've read about the theory of lattices of

subgroups. But I cannot interprete the output of the command

LatticeSubgroups(G) with G the permutationgroup.

Here's an example: G is the group of permutations of the triangle in the

plane.

GAP>LatticeSubgroups(G);

<subgroup lattice of Sym( [ 1 .. 3 ] ), 4 classes, 6 subgroups>

I don't understand how I can construct the full lattice when I know only

the number of Conjugacy Classes and the number of Subgroups.

Thank you for helping me

-----Ursprüngliche Nachricht-----

Von: GAP-Forum-Sender@dcs.st-and.ac.uk

[mailto:GAP-Forum-Sender@dcs.st-and.ac.uk]Im Auftrag von Bjorn

Vandenbergh

Gesendet: Donnerstag, 23. November 2000 16:36

An: Multiple recipients of list

Betreff: Subgroup Lattice??

Hello,

I'm a last years student in mathematics and I'm making my thesis. The

name will probably be "Working algebraic with groups: an acquintance

with Gap". In this matter I'm studying the Lattice of subgroups of a

permutation group with Gap. I've read about the theory of lattices of

subgroups. But I cannot interprete the output of the command

LatticeSubgroups(G) with G the permutationgroup.

Here's an example: G is the group of permutations of the triangle in the

plane.

GAP>LatticeSubgroups(G);

<subgroup lattice of Sym( [ 1 .. 3 ] ), 4 classes, 6 subgroups>

I don't understand how I can construct the full lattice when I know only

the number of Conjugacy Classes and the number of Subgroups.

Thank you for helping me

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