# Questions tagged [group-theory]

Questions on the group-theoretic functionality of Mathematica.

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### Make GroupOrbits recognise same orbit

When going through a list of elements, GroupOrbits usually recognises if the orbit of an element has been calculated already and will skip it in that case to avoid ...
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### How to determine if a group H is a normal subgroup of group G?

A subgroup $H$ of the group $G$ is normal group in $G$ if and only if $\displaystyle ghg^{-1}\in H$ for all $\displaystyle g\in G$ and $\displaystyle h\in H$. How to use MMA to know the group $H$ is a ...
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### Finding invariant matrix given group elements

I have a question about speeding up / optimising the following calculation. I have a feeling there is a way to rewrite it but I can't quite see what to do. In $d=3$ dimensions, given a set of ...
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### Does Mathematica limit the size of a set of permutation group generators?

I tried to generate general and special linear groups PGL2 and PSL2 over finite fields using straightforward algorithms over finite fields: The generators are permutations defined as the additive ...
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### Finding sequence of group generators that yields group element

Here is my permutation group that acts on lists of length 4, defined in terms of four generators: ...
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### Symmetry unique atom coordinates

One thing I love about Mathematica is how easily I can go from the name of a molecule to estimated coordinates of its atoms, with a command like ...
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### How to compute with Mathematica the space representation of a group for a given point set?

A set of points $P = \{p_1,p_2,\dots\} \subset \mathbb{R}^3$ in 3D is given. A symmetry transformation $S \in \mathbb{R}^{3 \times 3}$ is considered here as a matrix which maps the elements of $P$ to ...
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### How to solve problem 599 of Project-Euler

Problem 599 of the Project-Euler is described as follows: The well-known Rubik's Cube puzzle has many fascinating mathematical properties. The 2×2×2 variant has 8 cubelets with a total of 24 visible ...
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### Calculating Rubiks $2 \times 2 \times 2$ Permutation using Cycles

The help page of PermutationGroup shows a neat example on calculating the permutations of a $3\times 3\times 3$: ...
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### Illustration of Motzkin numbers: how to delete duplicates

The $n$-th Motzkin number is the number of different ways of drawing non-intersecting chords between $n$ points on a circle (not necessarily touching every point by a chord -- see https://en.wikipedia....
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### How to use Mathematica to prove that isotropic materials have only two independent parameters

Posts on related issues can be found from here or here. Index symmetries: A stiffness tensor $C$ is a fourth-order tensor with components $c_{ijkl}$ which maps symmetric second-order tensors into ...
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### Delete duplicates when cycle both position and element

Cycle of position means: {a, b, a, a} and {a, a, b, a} is the same. Cycle of element means: ...
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1 vote
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### How to evaluate an expression [closed]

I have a 3-dimensional array of numbers say A. I want to evaluate the following expression. $\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...
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### What is the cycle index polynomial for the trivial group

CycleIndexPolynomial[Cycles[{}], {Subscript[x, 1]}] returns 1. I was expecting ...
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### What does this graph mean?

Mathematica 11.3.0 includes a new command FindEquationalProof having good prospects. Studying it, I consider a somewhat modified example from the help ...
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