# Questions tagged [group-theory]

Questions on the group-theoretic functionality of Mathematica.

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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: ...
138 views

### 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 ...
30 views

### 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 ...
105 views

### 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 ...
89 views

### 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 $3\times 3\times 3$: ...
14 views

### Why does FiniteGroupData[{“SymmetricGroup”, 5}, “ConjugacyClasses”] return Missing[NotAvailable]?

This command works as I expected: FiniteGroupData[{"SymmetricGroup", 5}, "ConjugacyClassSizes"] {1, 10, 15, 20, 20, 30, 24} However, this one does not: ...
69 views

### Motzkin circles with rotational symmetry

Motzkin Circle means circles that any strings in a circle do not intersect. If we consider rotation symmetry, the rotation coincidence is the same, how to delete duplicate graphics? Following is the ...
264 views

### 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 ...
74 views

### 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: ...
49 views

### 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 ...
44 views

### What is the cycle index polynomial for the trivial group

CycleIndexPolynomial[Cycles[{}], {Subscript[x, 1]}] returns 1. I was expecting ...
168 views

### $GL(n,C)$ as a Lie group [closed]
I understand that $SO(3)$, $SU(3)$ are Lie groups since they are associated with rotations (The S excludes reflection). Why is $GL(n,C)$ also a Lie group?