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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

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?

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?


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?

a*b - b*a    where a , b are permutation group

how to minus this?

if a + b , then how to plus permutation group

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? 

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 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

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.


Dear friends, I recently answered a query concerning the action of the automorphism group of the Petersen graph on its edges at 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. ...

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....

Is there a possibility in Maple to define a set of elements using a rule or semanticdescription. The problem is that  I need to define a set of numbers of the concrete form (e.g. of the form a+b\sqrt[3](2)). Or more complecated task: the set of pairs (a,b) where a,b::integer. And then I need to define an abstract operation on that set. I explain: my global task is to create a procedure to define whether a set with an operation is a group (where a set is defined using a rule).

A simple question. I have this:



And I want to group it by x, y, z, so that I would get:



I'm using Maple 11.

I'm trying to make a Cayley table with a group of permutations (Specifically S3 and A4) and can't figure it out.  I've been looking through the help without much success.  Here is the code I have so far:


Matrix(nops(permgroup(6, {[[1, 2]], [[2, 3]]})), proc (i, j) options operator, arrow; multperms(i, j, permgroup(6, {[[1, 2]], [[2, 3]]})) end proc)



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