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Power Group Enumeration (update)....

June 19 2014
1 0

Greetings to all.

As some of you may remember I have posted several announcements concerning Power Group Enumeration and the Polya Enumeration Theorem this past year, e.g. at this MaplePrimes link: Power Group Enumeration.

I have continued to work in this field and for those of you who have followed the earlier threads I would like to present some links to my more recent work using the Burnside lemma. Of course all of these are programmed in Maple and include the Maple code and it is with the demonstration of Maple's group theory capabilities in mind that I present them to you (math.stackexchange links).

With my best wishes for happy group theory computing with Maple,

Regards,

Marko Riedel

Frobenius Groups...

June 16 2014
1 1

Does there exist a Frobenius Group which is not  neither a Dihedralgroup nor  Symm(3) ?

Best regards

Kurt Ewald

which theory can explain the interaction of compos...

May 28 2014
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which theory can explain the interaction of composition of group for combination of composition of group

if succeed to search a list of groups, what is the next step research them?

permutation group S_n for given n : cycle, tran...

May 07 2014
1 3

Hi,

I would like to compute the elements of the permutation group, let us say S10 or S20.

Is there any method to compute all the elements.

And can we make a list of the tranposition and cycles.

Many thinks.

how to join or meet for words of permutation group...

March 19 2014
0 0

for example

a*b v a^-1 = b

i guess Disj or Conj are Max or Min respectively

however i do not know how to max(a,b) where a and b are permutation group

reference from L group in

if can not calculate this, do not know how to determine whether equal in a*b v a^-1 = b

which rules or theorems can guide to generate rela...

March 03 2014
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1.which rules or theorems can guide to generate relations for words in group theory?

2.Is topological method such as complexes the direction to answer Question 1?

How to do composition for finite group...

February 28 2014
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How to do composition for finite group?

is the composition like permutation group ?

if express finite group like permutation group,

if so, can elements in first row duplicate? can the second row duplicate?

however, do not know how to map when there are more than or equal two choices

my guess is that

if finite group can be expressed into permutation group

for example 3*3 matrx, each column is a permutation group

then there will be 3 permutation groups, when do composition , first column's permutation group composite with first column's permutation group , second composite with second etc

is it right?

If do not have subgroup or normal subgroup, how to...

February 28 2014
1 0

i understand quotient group is

G/(normal subgroup)

= G composite with inverse permutation group of normal subrgoup

is this understanding correct?

If do not have subgroup or normal subgroup, how to do quotient group?

if i shift second row many times in order to find Subgroup satisfy G*Subgroup = Subgroup*G

after find Subgroup then test

inverse(g)*Subgroup*g = Subgroup

how to test whether inverse(g)*Subgroup*g belong to Subgroup?

or just use equal in inverse(g)*Subgroup*g = Subgroup?

how to plus or minus two permutation group...

February 28 2014
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a*b - b*a    where a , b are permutation group

how to minus this?

if a + b , then how to plus permutation group

How to solve word equation for permutation group...

February 26 2014
0 2

assume the word equation is

a_i *a_j - a_j *a_i = 0

how to find which permutation group is a_i and a_j

my understanding is to try all rotations

a book use underscript i and j

can i see them as upper script for i rotations which is shift i times to left for second row

and try all combination and composite them in two for loop?

Power Group Enumeration with Maple....

December 17 2013
3 0

Greetings to all.

This past year I have on occasion shared mathematical adventures with cycle index computations and Maple, e.g. at these links:

Befitting the season I am sending another post to continue this series of cycle index computations. I present two Maple implementations of Power Group Enumeration as described by Harary and Palmer in their book "Graphical Enumeration" and by Fripertinger in his paper "Enumeration in Musical Theory." It was a real joy working with Maple to implement the computational aspects of their work, i.e. the Power Group Enumeration Theorem. Moreover the resulting software is easy to read, simple and powerful and has a straightforward interface, taking advantage of many different capabilities present in Maple.

The problem I am treating is readily described. Consider a cube in 3 space and its symmetries under rotation, i.e. rigid motions. We ask in how many different ways we may color the edges of the cube with at most N colors where all colors are completely interchangable, i.e. have the symmetric group acting on them in addition to the edge permutation group of the cube. At the following Math Stackexchange Link  I have posted the Maple code to implement the algorithms / formulas of Harary / Palmer / Fripertinger to solve this problem. The reader is invited to study and test these algorithms. It seems to me an excellent instance of computational combinatorics fun.

To conclude I would like to point out that these algorithms might be candidates for a Polya Enumeration Theorem (PET) package that I have been suggesting for a future Maple release at the above posts, the algorithms being of remarkable simplicity while at the same time providing surprisingly sophisticated combinatorics and enumeration methods.

Season's greetings!

Marko Riedel

Does N variables caylay table have N permutation g...

November 04 2013
0 1

Does N variables caylay table have N permutation group so that can generate N functions?

for exmaple 3 variables cayley table have 3 permutation group, for 1, it has a permutation group , for 2 has a permutation group etc.

then does it mean that it has 3 functions, do it need to composite 3 functions in order to get a function belong to this cayley table?

1 1 1

1 2 2

1 2 3

how to divide or split an execution group at any p...

November 01 2013
1 2

I am not able to find way to do this very basic and common operation.

I use worksheet mode, and many times I'd like to split/divide a large execution group I've build of some code to 2 execution groups at some place. i.e. I'd like to point my mouse at a line and say divide here. Here is an example:

I see only the options Insert->Execution group-> After Cursor or Before cursor. Both of which do not do what I want. I want to divide it at that point.  So what I end up doing is to make a new execution group manually (using the Insert command), then go back and cut and paste the code I want in the new group.

I hope there is an option to do this. I do these sorts of things all the time when using Mathematica, which has Divide cell, Merge cells and other options. A cell in Mathematica is similar to execution group in Maple. Are there other options to maniuplate execution groups other insert before/after cursor that I might have missed? I am using 17.02 on windows 7.

Please note, I only use worksheet mode.

automorphisms of the petersen graph...

January 21 2013 Maple
4 3

Dear friends, I recently answered a query concerning the action of the automorphism group of the Petersen graph on its edges at stackexchange.com. The algorithm that I present is quite naive, but it does produce the desired result. I thought I would share it here because it makes a nice Maple programming exercise e.g. for a talented student at high school level. ...

Galois group with parameters...

November 12 2012
1 1

I consider a polynomial \$P(x)\$ such that their coefficients are in \$\mathbb{Q}(u_1,\cdots,u_k)\$ where \$u_1,\cdots,u_k\$ are complex parameters. I use in Maple the command \$galois(p(x),x)\$ and I obtain a fixed Galois group solution.  Fortunately, when I give explicit values (randomly chosen) to the \$(u_i)_i\$, I obtain always the previous group as Galois group. I think that Maple considers that the \$(u_i)_i\$ satisfy no algebraic equations, that is the \$(u_i)_i\$ are generic....

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